Honors Physics B Unit 1 Exam

A standing wave is produced by plucking a string. The points along the plucked string that appear not to be vibrating are produced by ___ interference.

(complete) destructive

Section 4: Wave Interactions (Section Objectives)

- Apply the superposition principle. - Differentiate between constructive and destructive interference. - Predict when a reflected wave will be inverted. - Predict whether specific traveling waves will produce a standing wave. - Identify nodes and antinodes of a standing wave.

Section 3: Properties of Waves (Key Ideas)

- As a wave travels, the particles of the medium vibrate around an equilibrium position. - In a transverse wave, vibrations are perpendicular to the direction of wave motion. In a longitudinal wave, vibrations are parallel to the direction of wave motion. - Wave speed equals frequency times wavelength.

Chapter 15 Section 1 Objectives

- Describe how light waves interfere with each other to produce bright and dark fringes. - Identify the conditions required for interference to occur. - Predict the location of interference fringes using the equation for double-slit interference.

Chapter 15 Section 3 Objectives

- Describe the properties of laser light. - Explain how laser light has particular advantages in certain applications

By what factor should the length of a simple pendulum be changed in order to triple the period of vibration?

9

A noisy machine in factory produces a decibel rating of 80 dB. How many identical machines could you add to the factory without exceeding the 90 dB limit set by federal regulations?

9 machines (for a total of 10)

Period of a Simple Pendulum in Simple Harmonic Motion

T = 2π√L/ag - period = 2π × square root of (length divided by free-fall acceleration)

Period of a Mass-Spring System in Simple Harmonic Motion

T = 2π√m/k - period = 2π × square root of (mass divided by spring constant)

Which additive colors affect the color of light?

The additive colors that affect the color of light are red, green, and blue.

Linear Polarization

The alignment of electromagnetic waves in such a way that the vibrations of the electric fields in each of the waves are parallel to each other

What feature of a wave increases when the source of vibration increases in energy?

The amplitude increases.

Electric guitars, which use electric amplifiers to magnify their sound, can have a variety of shapes, but acoustic guitars all have the same basic shape. Explain why.

The body of an acoustic guitar is designed so that it can transmit the strings' vibrations to the air efficiently. (The guitar's particular shape also determines the characteristic sound that distinguishes the guitar from similar instruments, such as banjos and lutes.) Because the vibrations of an electric guitar's strings are converted into electrical signals, there are fewer restrictions on the electric guitar's shape.

Coherence

The correlation between the phases of two or more waves

Path Difference

The difference in the distance traveled by two beams when they are scattered in the same direction from different points

Wavelength (λ)

The distance between two adjacent similar points of a wave, such as from crest to crest or from trough to trough

As a wave travels, what happens to the particles in the medium it travels through?

The particles of the medium vibrate around an equilibrium position.

On what does the period of a mass-spring system depend?

The period depends only on the mass and the spring constant.

On what does the period of a pendulum depend?

The period depends only on the string length and the free-fall acceleration.

A simple pendulum can be used as an altimeter on a plane. How will the period of the pendulum vary as the plane rises from the ground to its final cruising altitude?

The period will increase as the altitude increases.

Which of the following wavelengths will produce standing waves on a string that is 3.5 m long? a. 1.75 m b. 3.5 m c. 5.0 m d. 7.0 m

a, b, and d (λ = 0.5L, L, and 2L, respectively)

Anthony sends a series of pulses of amplitude 24 cm down a string that is attached to a post at one end. Assuming the pulses are reflected with no loss of amplitude, what is the amplitude at a point on the string where two pulses are crossing if a. the string is rigidly attached to the post? b. the end at which reflection occurs is free to slide up and down?

a. 0.0 cm b. 48 cm

Using the superposition principle, draw the resultant waves for each of the examples below.

a. a sine wave with twice the amplitude b. a straight line (the waves cancel each other completely)

On the planet Xenos, an astronaut observes that a 1.00 m long pendulum has a period of 1.50 s. What is the free-fall acceleration on Xenos?

17.6 m/s²

In a double-slit interference experiment, a wave from one slit arrives at a point on a screen one wavelength behind the wave from the other slit. What is observed at that point?

bright fringe

Of the following materials, sound waves travel fastest through

copper at 0°C.

Each compression in the waveform of the longitudinal wave shown above corresponds to what feature of the transverse wave below it? - wavelength - crests - troughs - amplitude

crests

Decibel Level

dB - decibels

The speed of sound...

depends on the medium.

The frequency of a sound wave...

determines its pitch.

Vibration of an object about an equilibrium point is called simple harmonic motion when the restoring force is proportional to

displacement.

Alignment of electromagnetic waves in such a way that the vibrations of the electric fields in each of the waves are parallel to each other is called

linear polarization

In a stretched spring, several coils are pinched together and others are spread farther apart than usual. What sort of wave is this?

longitudinal

L; Length of a vibrating string or an air column

m - meters

List four examples of simple harmonic motion.

mass-spring system, child on a swing, pendulum of a grandfather clock, metronome

What is common to all waves?

movement of a disturbance

Two tuning forks with frequencies of 256 Hz and 512 Hz are struck. Which of the sounds will move faster through the air?

neither, because the speed of sound is constant in air.

The human ear transmits vibrations that cause...

nerve impulses.

Each stretched region in the waveform of the longitudinal wave shown above corresponds to what feature of the transverse wave below it?

trough

A child swings on a playground swing. How many times does the child swing through the swing's equilibrium position during the course of a single period of motion?

twice

How does a single point on a string move as a transverse wave passes by that point?

up and down, no horizontal movement

Speed of a Wave

v = fλ - speed of a wave = frequency × wavelength

A mass attached to a spring vibrates back and forth. At the equilibrium position, the - acceleration reaches a maximum. - velocity reaches a maximum. - net force reaches a maximum. - velocity reaches zero.

velocity reaches a maximum

What type of image is formed from a convex spherical mirror?

vertical image, smaller than object

The superposition of mechanical waves can be observed in the movement of

water waves in a ripple tank.

Section 3: Properties of Waves (Section Objectives)

- Distinguish local particle vibrations from overall wave motion. - Differentiate between pulse waves and periodic waves. - Interpret waveforms of transverse and longitudinal waves. - Apply the relationship among wave speed, frequency, and wavelength to solve problems. - Relate energy and amplitude.

Knowledge to Review (Chapter 11)

- Elastic potential energy is the energy stored in a stretched or compressed elastic object. - A spring constant is a parameter that expresses how resistant a spring is to being compressed or stretched. - Gravitational potential energy is the energy associated with an object due to its position relative to Earth.

Section 2: Measuring Simple Harmonic Motion (Section Objectives)

- Identify the amplitude of vibration. - Recognize the relationship between period and frequency. - Calculate the period and frequency of an object vibrating with simple harmonic motion.

Section 1: Simple Harmonic Motion (Section Objectives)

- Identify the conditions of simple harmonic motion. - Explain how force, velocity, and acceleration change as an object vibrates with simple harmonic motion. - Calculate the spring force using Hooke's law.

Section 4: Wave Interactions (Key Ideas)

- If two or more waves are moving through a medium, the resultant wave is found by adding the individual displacements together point by point. - Standing waves are formed when two waves that have the same frequency, amplitude, and wavelength travel in opposite directions and interfere.

Section 1: Simple Harmonic Motion (Key Ideas)

- In simple harmonic motion, restoring force is proportional to displacement. - A mass-spring system vibrates with simple harmonic motion, and the spring force is given by Hooke's law. - For small angle of displacement (<15°), a simple pendulum swings with simple harmonic motion. - In simple harmonic motion, restoring force and acceleration are maximum at maximum displacement and speed is maximum at equilibrium.

Chapter 15 Overview

- Section 1 identifies the conditions required for interference to occur and shows how to calculate the location of bright and dark fringes in double-slit interference. - Section 3 describes how a laser produces coherent light and explores applications of lasers.

Chapter 11 Overview

- Section 1 introduces restoring force, the conditions of simple harmonic motion, Hooke's law, and the relationship between force, velocity, and acceleration is simple harmonic motion. - Section 2 identifies the variables affecting amplitude, period, and frequency in a simple pendulum and in a mass-spring system. - Section 3 introduces concepts of wave motion, including wave speed, frequency, wavelength, amplitude, and energy, and discusses their relationships. - Section 4 explores how to use the superposition principle to predict patterns of interference and to identify the conditions for standing waves.

Section 2: Measuring Simple Harmonic Motion (Key Ideas)

- The period of a mass-spring system depends only on the mass and the spring constant. The period of a simple pendulum depends only on the string length and the free-fall acceleration. - Frequency is the inverse of period.

Chapter 15 Knowledge to Review

- The superposition principle: When two mechanical waves pass through the same space at the same time, their displacements at each point add. - When two waves with the same frequency and amplitude overlap, the resulting wave has the same frequency as the individual waves. If the waves are in phase, the resultant wave has twice their amplitude. If they are 180° out of phase, the amplitudes cancel.

Equation for Destructive Interference

- dsinθ = ±(m + 1/2)λ; m = 0, 1, 2, 3,... - the path difference between two waves = an odd number of half wavelengths

Equation for Constructive Interference

- dsinθ = ±mλ; m = 0,1,2,3,... - the path difference between two waves = an integer multiple of the wavelength

How much displacement will a coil spring with a spring constant of 120 N/m achieve if it is stretched by a 60 N force?

-0.5 m

A string is rapidly attached to a post at one end. Several pulses of amplitude 0.15 m sent down the string are reflected at the post and travel back down the string without a loss of amplitude. What is the amplitude at a point on the string where the maximum displacement points of two pulses cross? What type of interference is this?

0.00 m; destructive

What is the wavelength of microwaves of 3.0 × 10⁹ Hz frequency?

0.10 m

A wave of amplitude 0.30 m interferes with a second wave of amplitude 0.20 m. What is the largest resultant displacement that may occur?

0.30 m + 0.20 m = 0.50 m

How would your answer to item 2 change if the same pulses were sent down a string whose end is free? What type of interference is this?

0.30 m; constructive

What are the 3 steps in drawing ray diagrams?

1. Draw a ray from the top of the object, parallel to the axis. It will then reflect off of the mirror back through the focal point. 2. Draw a ray from the top of the object through the focal point of the mirror. It will then be reflected parallel to the axis from the mirror. 3. Draw a ray through the center of curvature of the mirror (two times the focal length.) It will be reflected from the mirror back along itself.

If you shook the end of a rope up and down three times each second, what would be the period of the waves set up in the rope? What would be the frequency?

1/3 s; 3 Hz

Which equation is correct for calculating the focal point for a spherical mirror?

1/f = 1/p + 1/q

What is the mirror equation?

1/p + 1/q = 1/f; Where p is the object distance, q is the image distance, and f is the focal length of the mirror.

A musical tone sounded on a piano has a frequency of 261.6 Hz and a wavelength of 1.31 m. What is the speed of the sound wave?

343 m/s

Look at the standing wave shown in Figure 22. How many nodes does this wave have? How many antinodes?

4 nodes; 3 antinodes

A vibrating guitar string emits a tone just as a 5.00 × 10² Hz tuning fork is struck. If five beats per second are heard, which of the following is a possible frequency of vibration of the string?

495 Hz

What is the total distance traveled by an object moving back and forth in simple harmonic motion in a time interval equal to its period when its amplitude is equal to A?

4A

Laser

A device that produces coherent light at a single wavelength

Decibel

A dimensionless unit that describes the ratio of two intensities of sound; the threshold of hearing is commonly used as the reference intensity

What produces resonance?

A forced vibration at the natural frequency produces resonance.

What is the relationship between frequency and pitch?

A greater frequency is perceived as a higher pitch.

How do humans perceive sound?

A human ear transmits vibrations that cause nerve impulses. The brain interprets these impulses as sounds of varying frequencies.

What is a laser?

A laser is a device that transforms energy into a beam of coherent monochromatic light.

Pitch

A measure of how high or low a sound is perceived to be, depending on the frequency of the sound wave

Resonance

A phenomenon that occurs when the frequency of a force applied to a system matches the natural frequency of vibration of the system, resulting in a large amplitude of vibration

Medium

A physical environment through which a disturbance can travel

How do an open pipe and a closed pipe differ in terms of the harmonics they produce?

A pipe open at both ends produces all harmonics. A pipe closed at one end produces only odd-numbered harmonics.

Node

A point in a standing wave that maintains zero displacement

Antinode

A point in a standing wave, halfway between two nodes, at which the largest displacement occurs

What is the difference between a pulse wave and a periodic wave?

A pulse wave is a single traveling disturbance resulting from a motion that is not repeated. A periodic wave is one whose source is repeated motion.

What is the difference between a real and virtual image?

A real image is formed by actual light rays passing through the image, and a real image can be made visible on a physical surface. A virtual images is the apparent reproduction of an image and cannot be made visible on a physical surface.

Harmonic Series

A series of frequencies that includes the fundamental frequency and integral multiples of the fundamental frequency

Constructive Interference

A superposition of two or more waves in which individual displacement on the same side of the equilibrium position are added together to form the resultant wave

Destructive Interference

A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave

Standing Wave

A wave pattern that results when two waves of the same frequency, wavelength, and amplitude travel in opposite directions and interfere

Mechanical Wave

A wave that requires a medium through which to travel

Longitudinal Wave

A wave whose particles vibrate parallel to the direction the wave is traveling

Transverse Wave

A wave whose particles vibrate perpendicularly to the direction the wave is traveling

Which is not correct when describing the formation of rainbows?

All wavelengths refract at the same angle.

Doppler effect

An observed change in frequency when there is relative motion between the source of waves and an observer

What do we call the angle between the ray that strikes a surface and the line perpendicular to the surface at the point of contact?

Angle of Incidence

What does Snell's law state?

As a light ray travels from one medium to another, the light ray will change its direction unless it travels along the normal.

The fundamental frequency of any note produced by a flute will vary slightly with temperature changes in the air. For any given note, will an increase in temperature produce a slightly higher fundamental frequency or a slightly lower one?

As temperature increases, the speed of sound in air increases. Because f₁ is proportional to v, fundamental frequency likewise increases.

In preparing to shoot an arrow, an archer pulls a bowstring back 0.40 m by exerting a force that increases uniformly from 0 to 230 N. What is the equivalent spring constant of the bow?

Givens: x = -0.40 m, F = 230 N Solution: k = -F/x k = -230 N/-0.40 m k = 580 N/m

Light waves travel nearly 1 million times faster than sound waves in air. With this in mind, explain how the distance to a lighting bolt can be determined by counting the seconds between the flash and the sound of the thunder.

Because light travels so much faster than sound, the speed of light can be considered to be effectively infinite in this case, and the flash is considered to have occurred at the same instant we see it. Thus, the time it takes the sound wave to reach the listener multiplied by the speed of sound in air gives the approximate distance between the observer and the lightning bolt.

How do you describe the motion of both a mass-spring system and a pendulum with a small angle of displacement?

Both of these types of motion are simple harmonic motion.

Find the Critical Angle

Coherence (Lasers)

Which type of mirror can form a real image?

Concave

Explain decibel level.

Decibel level is a measure of relative intensity on a logarithmic scale.

What is dispersion?

Dispersion is referred to as the process by which polychromatic light is separated into its component wavelengths. The most common example of dispersion is when white light strikes a prism, causing it to fan out into a series of colors.

Hooke's Law

Felastic = -kx - spring force = -(spring constant × displacement)

An upright pencil is placed in front of a convex spherical mirror with a focal length of 8.00 cm. An erect image 2.50 cm tall is formed 4.44 cm behind the mirror. Find the position of the object, the magnification of the image, and the height of the pencil.

Focal Length = 10.0 cm p = +30.0 cm 1/p + 1/q = 1/f; M = - q/p 1/q = 1/f - 1/p 1/q = 1/10.0 cm - 1/30.0 cm = 0.100/1 cm - 0.033/1 cm = 0.067/1 cm q = 1/0.067 = 14.9 M = - q/p = - 14.9 cm/30.0 cm = -0.49 cm

If the wavelength of a sound source is reduced by a factor of 2, what happens to the wave's frequency? What happens to its speed?

Frequency doubles; Speed remains constant.

What is the difference between frequency and pitch?

Frequency is an objective measure of the rate of particle vibration. Pitch is a subjective quality that depends on the listener.

How does frequency relate to period?

Frequency is the inverse of period.

Vibration of a certain frequency produces a standing wave on a stretched string that is 2.0 m long. The standing wave has 7 nodes and 5 antinodes. What is the wavelength of the wave that produces this standing wave?

Given: L = 2.0 m; The standing wave has 5 antinodes, i.e., 5 loops Solution: A single loop (antinode) is produced by a wavelength equal to 2L. Two loops (one complete wavelength) are produced by a wavelength of L. A wavelength of 2/3 L results in 3 antinodes. The following pattern emerges: 1 loop λ = 2L/1 = 2L 2 loops λ = 2L/2 = L 3 loops λ = 2L/3 = 2/3 L 4 loops λ = 2L/4 = 1/2 L 5 loops λ = 2L/5 = 2/5 L 2/5 × 2.0 m = 0.80 m

You dip your finger into a pan of water twice each second, producing waves with crests that are separated by 0.15 m. Determine the frequency, period, and speed of these water waves.

Given: λ = 0.15 m Solution: Because a wave is generated twice each second, f = 2.0 Hz T = 1/f = 1/2.0 Hz = 0.50 s v = λf = (0.15 m)(2.0 Hz) = 0.30 m/s

What is the free-fall acceleration in a location where the period of a 0.850 m long pendulum is 1.86 s?

Givens: L = 0.850 m, T = 1.86 s Solution: T = 2π√L/ag ag = 4π²L/T² = (4π²)(0.850 m)/(1.86 s)² = 9.70 m/s²

A student wishes to construct a mass-spring system that will oscillate with the same frequency as a swinging pendulum with a period of 3.45 s. The student has a spring with a spring constant of 72.0 N/m. What mass should the student use to construct the mass-spring system?

Givens: Tpendulum = 3.45 s, k = 72.0 N/m Solution: If both systems have the same frequency, they will also have the same period. Therefore, the given period may be substituted into the equation for a mass-spring system. T = 2π√m/k T² = 4π²(m/k) m = T²k/4π² = (3.45 s)²(72.0 N/m)/4π² m = 21.7 kg

A certain pendulum clock that works perfectly on Earth is taken to the moon, where ag = 1.63 m/s². If the clock is started at 12:00 A.M., what will it read after 24.0 h have passed on Earth?

Givens: ag,moon = 1.63 m/s², ∆t = 24 h, ag,Earth = 9.81 m/s² Solution: TEarth = 2π√L/ag,Earth Tmoon = 2π√L/ag,moon Tmoon/TEarth = √ag,Earth/ag,moon = √9.81 m/s²/1.63 m/s² = 2.45 The clock on the moon runs slower than the same clock on Earth by a factor of 2.45. Thus, after 24.0 h Earth time, the clock on the moon will have advanced by 24.0 h/2.45 = 9.80 h = 9 h + (0.80 h)(60 min/h) = 9 h, 48 min - Thus, the clock will read 9:48 A.M.

Find the length of a pendulum that oscillates with a frequency of 0.16 Hz.

Givens: f = 0.16 Hz, ag = g = 9.81 m/s² Solution: T = 1/f = 2π√L/ag L = ag/(2πf)² = (9.81 m/s²)/(4π²)(0.16 Hz)² L = 9.7 m

Radio waves from an FM station have a frequency of 103.1 MHz. If the waves travel with a speed of 3.00 × 10⁸ m/s, what is the wavelength?

Givens: f = 103.1 MHz, v = 3.00 × 10⁸ m/s Solution f = 103.1 MHz = 1.031 × 10⁸ Hz v = fλ λ = v/f = (3.00 × 10⁸ m/s)/(1.031 × 10⁸ Hz) = 2.91 m

A wave traveling in the positive x direction with a frequency of 25.0 Hz is shown in the figure above. Find the following values for this wave: a. amplitude b. wavelength c. period d. speed

Givens: f = 25.0 Hz, 1/2λ = 10.0 cm, 2(amplitude) = 18 cm Solutions: a. amplitude = 18 cm/2 = 9.0 cm b. λ = (2)(10.0 cm) = 20.0 cm c. T = 1/f = 1/25.0 Hz = 0.0400 s d. v = λf = (0.200 m)(25.0 Hz) = 5.00 m/s

Bats chirp at high frequencies that humans cannot hear. They use the echoes to detect small objects, such as insects, as small as one wavelength. If a bat emits a chirp at a frequency of 60.0 kHz and the speed of sound waves in air is 340 m/s, what is the size in millimeters of the smallest insect that the bat can detect?

Givens: f = 60.0 kHz = 60.0 × 1000 = 60000 Hz; v = 340 m/s; wavelength (in millimeters) = ? Equation: v = f(frequency) × wavelength Work v = f(frequency) × wavelength 340 m/s = 60000 Hz × wavelength 340 m/s ÷ 60000 Hz = wavelength 0.005667 m = wavelength 0.005667 m × 1000 mm = wavelength 5.667 millimeters = wavelength Answer: So, the size in millimeters of the smallest insect that the bat can detect is 5.667 millimeters.

The notes produced by a violin range in frequency from approximately 196 Hz to 2637 Hz. Find the possible range of wavelengths in air produced by this instrument when the speed of sound in air is 340 m/s.

Givens: f₁ = 196 Hz, f₂ = 2637 Hz, v = 340 m/s Solution: λ₁ = v/f₁ = 340 m/s/196 Hz = 1.73 m λ₂ = v/f₂ = 340 m/s/2637 Hz = 0.129 m

In an arcade game, a 0.12 kg disk is shot across a frictionless horizontal surface by being compressed against a spring and then released. If the spring has a spring constant of 230 N/m and is compressed from its equilibrium position by 6.0 cm, what is the magnitude of the spring force on the disk at the moment it is released?

Givens: k = 230 N/m, x = -6.0 cm Solution F = -kx F = -(230 N/m)(-0.060 m) F = 14 N

Janet wants to find the spring constant of a given spring, so she hangs the spring vertically and attaches a 0.40 kg mass to the spring's other end. If the spring stretches 3.0 cm from its equilibrium position, what is the spring constant?

Givens: m = 0.40 kg, x = -3.0 m, g = 9.81 m/s² Solution: -kx - mg = 0 k = -mg/x = -(0.40 kg)(9.81 m/s²)/-0.030 m k = 130 N/m

A car with bad shock absorbers bounces up and down after hitting a bump. The car has a mass of 1500 kg and is supported by four springs, each having a spring constant of 6600 N/m. What is the period for each spring?

Givens: mtotal = 1500 kg, k(per spring) = 6600 N/m Solution: Assume that the total mass of 1500 kg is supported equally on the four springs. Each spring then supports 1500 kg/4. T = 2π√m/k = 2π√(1500 kg/4)/(6600 N/m) = 1.5 s

Yellow light travels through a certain glass block at a speed of 1.97 × 10⁸ m/s. The wavelength of the light in this particular type of glass is 3.81 × 10⁻⁷ m (381 nm). What is the frequency of the yellow light?

Givens: v = 1.97 × 10⁸ m/s, λ = 3.81 × 10⁻⁷ m Solution: f = v/λ = 1.97 × 10⁸ m/s/3.81 × 10⁻⁷ m = 5.17 × 10¹⁴ Hz

Microwaves travel at the speed of light, 3.00 × 10⁸ m/s. When the frequency of microwaves is 9.00 × 10⁹ Hz, what is their wavelength?

Givens: v = 3.00 × 10⁸ m/s; f = 9.00 × 10⁹ Hz Solution: λ = v/f = (3.00 × 10⁸ m/s)/(9.00 × 10⁹ Hz) = 0.0333 m

A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz. Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 m/s.

Givens: v = 340 m/s; f1 = 28 Hz; f2 = 4200 Hz Unknown: λ = ? Equation: v = fλ Solution: v = fλ λ = v/f1 = 320 m × s⁻¹/28 s⁻¹ = 12.14 = 12 m v = fλ λ = v/f2 = 340 m × s⁻¹/4200 s⁻¹ = 0.080952381 = 0.081 m 0.081 ≤ λ ≤ 12 m

A sound wave traveling at 343 m/s is emitted by the foghorn of a tugboat. An echo is heard 2.60 s later. How far away is the reflecting object?

Givens: v = 343 m/s, ∆t = 2.60 s Solution: ∆x = v∆t/2 = (343 m/s)(2.60 s)/2 = 446 m

A mass on a spring that has been compressed 0.1 m has a restoring force of 20 N. What is the spring constant?

Givens: x = -0.1 m, Felastic = 20 N Solution: Felastic = -kx k = -Felastic/x k = -20 N/-0.1 m = 200 N/m

A child's toy consists of a piece of plastic attached to a spring, as shown at right. The spring is compressed against the floor a distance of 2.0 cm and released. If the spring constant is 85 N/m, what is the magnitude of the spring force acting on the toy at the moment it is released?

Givens: x = -2.0 cm, k = 85 N/m Solution: F = -kx = -(85 N/m)(-0.020 m) F = 1.7 N

What are harmonics?

Harmonics are integral multiples of the fundamental frequency.

Dolphin echolocation is similar to ultrasound. Reflected sound waves allow a dolphin to form an image of the object that reflected the waves. Dolphins can produce sound waves with frequencies ranging from 0.25 kHz to 220 kHz, but only those at the upper end of this spectrum are used in echolocation. Explain why high-frequency waves work better than low-frequency waves.

Higher frequencies function well in echolocation because their relatively short wavelengths are able to detect smaller objects. (Longer wavelengths would disperse around small objects.)

fn; Frequency of the nth harmonic

Hz - Hertz = s⁻¹

What are the differences between a longitudinal wave and a transverse wave?

In a transverse wave, vibrations are perpendicular to the direction of wave motion. In a longitudinal wave, vibrations are parallel to the direction of wave motion.

What is the difference between constructive interference and destructive interference?

In constructive interference, individual displacements are on the same side of the equilibrium position. In destructive interference, the individual displacements are on opposite sides of the equilibrium position.

What are the differences between infrasonic, audible, and ultrasonic sound waves?

Infrasonic waves are below 20 Hz, audible waves are between 20 and 20000 Hz, and ultrasonic waves are greater than 20000 Hz.

Intensity of a Spherical Wave

Intensity = P/4πr² - Intensity = (power)/(4π)(distance from the source)²

What determines which sounds are audible?

Intensity and frequency determine which sounds are audible.

What is the difference between intensity and decibel level?

Intensity is power per area; decibel level is a measure of relative intensity.

What happens to the wavelength of a wave on a string when the frequency is doubled? What happens to the speed of the wave?

It becomes half as long; It stays the same.

What does an image formed by a converging lens look like?

It is real and inverted when the object is outside the focal point and virtual and upright when the object is inside the focal point.

Fiber-optic systems transmit light by means of internal reflection within thin strands of extremely pure glass. In these fiber-optic systems, laser light is used instead of white light to transmit the signal. Apply your knowledge of refraction to explain why.

Laser light is nearly monochromatic, so it does not spread out very much into different components with different wavelengths as it passes between the fiber and transmission and receiving equipment (that is, dispersion is nearly absent over short distances).

How are lasers used to determine the distance from Earth to the moon?

Lasers are used to determine the distance from Earth of the moon in that the distance from Earth to the moon is based on d = v/t, where d is equal to the speed of light of the laser, v, over the time it takes for the laser to reach the reflectors on the moon and back, t. Additionally, lasers can be used to measure large distances since they can be pointed towards distant reflectors, and the reflected light can be detected. So, laser light is directed at several points on the moon's surface.

What is light?

Light is electromagnetic radiation that consists of oscillating electric and magnetic fields with different wavelengths.

What is polarization?

Light is polarized when some of the rays are blocked by filters, and only one orientation of waves is permitted through the filter.

At what angle is light reflected from a flat mirror?

Light is reflected back from a flat mirror at an angle equal to the angle the incident ray made with the normal (a perpendicular line to the mirror surface.)

How is light reflected from a convex spherical mirror?

Light is reflected back from the mirror, and all rays diverge. Thus to form an image, our eyes perform an optical illusion and extend the rays back through the mirror towards the focal point.

How is light reflected from a concave spherical mirror?

Light is reflected back toward the object from a concave spherical mirror.

How are light and dark interference patterns formed by light waves?

Light waves with the same wavelength and constant phase differences interfere with each other to produce light and dark interference patterns.

How is linearly polarized light formed and detected?

Linearly polarized light is formed and detected through transmission, reflection, and scattering.

What helps explain natural phenomena like mirages and the visibility of the sun after it has set?

Many of these natural phenomena can be attributed to the refraction of light in the Earth's atmosphere.

Explain why the speed of sound depends on the temperature of the medium. Why is this temperature dependence more noticeable in a gas than in a solid or a liquid?

Molecules that have more motion (higher temperature) can transfer their vibrations more easily. This is less noticeable in liquids and solids because the particles are closer together.

In an old-fashioned pendulum clock, the bob is moved up and down to adjust the clock to keep accurate time. How would you adjust the bob in order to correct a clock that runs too fast? Explain why the adjustment works.

Moving the pendulum bob down increases the length of the pendulum. As a result, the period of the pendulum increases and the frequency decreases.

A pendulum is released 40° from its resting position. Is its motion simple harmonic?

No, a pendulum's displacement is approximately proportional to its restoring force only at angles smaller than 15°.

Does the acceleration of a simple harmonic oscillator remain constant during its motion? Is the acceleration ever zero? Explain.

No, acceleration changes throughout the oscillator's motion. It is zero at the equilibrium position and greatest at maximum displacement.

By listening to a band or an orchestra, how can you determine that the speed of sound is the same for all frequencies?

Notes that are played at the same time reach your ears at the same time.

Opera singers have been known to set crystal goblets in vibration with their powerful voices. In fact, an amplified human voice can shatter the glass, but only at certain fundamental frequencies. Speculate about why only certain fundamental frequencies will break the glass.

Only frequencies that match one of the natural frequencies of the glass can establish a resonance condition. Only then can the vibrations become large enough to shatter the goblet.

How do pigments affect the color of reflected light?

Pigments affect the color of reflected light in that the pigments rely on colors of light that are absorbed, or subtracted, from the incoming light.

Federal regulations require that no office or factory worker be exposed to noise levels that average above 90 dB over an 8 h day. Thus, a factory that currently averages 100 dB must reduce its noise level by 10 dB. Assuming that each piece of machinery produces the same amount of noise, what percentage of equipment must be removed? Explain your answer.

Reducing the decibel level by 10 requires reducing the intensity by a factor of 10. Thus, 90 percent of the equipment must be removed.

In simple harmonic motion, when are the restoring force and acceleration at a maximum? When is speed at a maximum?

Restoring force and acceleration are at a maximum at maximum displacement and speed is maximum at equilibrium.

How does the restoring force relate to displacement in simple harmonic motion?

Restoring force is proportional to displacement.

Explain why sound intensity is inversely proportional to the square of the distance from the source.

Sound intensity is inversely proportional to the square of the distance from the source because the same energy is spread over a larger area.

As a result of a distant explosion, an observer first senses a ground tremor, then hears the explosion. What accounts for this time lag?

Sound travels faster through the ground.

Sound pulses emitted by a dolphin travel through 20°C ocean water at a rate of 1450 m/s. In 20°C air, these pulses would travel 342.9 m/s. How can you account for this difference in speed?

Sound waves travel faster through water than through air because the molecules of water are closer together and, as a result, can spread vibrations more quickly.

How are standing waves formed?

Standing waves are formed when two waves that have the same frequency amplitude and wavelength travel in opposite directions and interfere.

As a dolphin swims toward a fish, the dolphin sends out sound waves to determine the direction the fish is moving. If the frequency of the reflected waves is higher than that of the emitted waves, is the dolphin catching up to the fish or falling behind?

The dolphin is catching up to the fish.

A flute is similar to a pipe open at both ends, while a clarinet is similar to a pipe closed at one end. Explain why the fundamental frequency of a flute is about twice that of the clarinet, even though the length of these two instruments is approximately the same.

The first possible wavelength is 2L for the flute and 4L for the clarinet. Because the speed of sound is the same in each and v = λf, the flute's fundamental frequency is twice the clarinet's.

What is the focal point (f) for a convex spherical mirror?

The focal point for a convex spherical mirror is behind the mirror, and thus is negative.

In pinball games, the force exerted by a compressed spring is used to release a ball. If the distance the spring is compressed is doubled, how will the force exerted on the ball change? If the spring is replaced with one that is half as stiff, how will the force acting on the ball change?

The force will double; The force will be half as large.

What determines pitch?

The frequency of a sound wave determines its pitch.

What is the relationship between frequency, wavelength, and the speed of light?

The frequency times the wavelength of electromagnetic radiation is equal to c, the speed of light.

A pendulum bob is made with a ball filled with water. What would happen to the frequency of vibration of this pendulum if a hole in the ball allowed water to slowly leak out? (Treat the pendulum as a simple pendulum.)

The frequency would not change, because the frequency of a simple pendulum does not depend on mass.

Why does a vibrating guitar string sound louder when it is on the instrument than it does when it is stretched on a work bench?

The guitar's body transfers the string's vibrations to the air more efficiently, which increases the intensity of the sound.

Crest

The highest point above the equilibrium position

Explain why a saxophone sounds different from a clarinet, even when they sound the same fundamental frequency at the same decibel level.

The instruments have different harmonics present at various intensity levels.

What happens when a light ray travels from a medium of a smaller refractive index to one of a higher refractive index?

The light ray bends toward the normal.

What technique can you use to find the location of an image formed by a lens?

The location of an image created by a lens can be found using either a ray diagram or the thin-lens equation.

Fundamental Frequency

The lowest frequency of vibration of a standing wave

Trough

The lowest point below the equilibrium position

Amplitude

The maximum displacement from the equilibrium

Timbre

The musical quality of a tone resulting from the combination of harmonics present at different intensities

What is timbre?

The number and intensity of harmonics that account for the sound quality of an instrument.

Order Number

The number assigned to interference fringes with respect to the central bright fringe

Frequency

The number of cycles or vibrations per unit of time

Beat

The periodic variation in the amplitude of a wave that is the superposition of two waves of slightly different frequencies

Intensity

The rate at which energy flows through a unit area perpendicular to the direction of wave motion

Compression

The region of a longitudinal wave in which the density and pressure are at a maximum

Rarefaction

The region of a longitudinal wave in which the density and pressure are at a minimum

What causes the Doppler effect?

The relative motion between the source of waves and an observer creates an apparent frequency shift known as the Doppler effect.

In an oscillating mass-spring system, the restoring force is a result of the force exerted by the spring. What causes the restoring force in a swinging pendulum?

The restoring force in a swinging pendulum is a component of the gravitational force acting on the pendulum bob.

If two or more waves are moving through a medium, how do you find the resultant wave?

The resultant wave is found by adding the individual displacements together point by point.

You are at a street corner and hear an ambulance siren. Without looking, how can you tell when the ambulance passes by?

The siren's pitch will drop.

The decibel level of an orchestra is 90 dB, and a single violin achieves a level of 70 dB. How does the sound intensity from the full orchestra compare with that from the violin alone?

The sound intensity from the orchestra is 100 times that from the violin.

What is the sound intensity of a spherical wave?

The sound intensity of a spherical wave is the power per area.

What affects the speed of sound?

The speed of sound depends on the medium through which it travels.

In a mass-spring system how do you calculate the spring force?

The spring force is given by Hooke's law (Felatstic = - kx).

Why are pushes given to a playground swing more effective if they are given at certain, regular intervals than if they are given at random positions in the swing's cycle?

The swing's amplitude is maximized when the pushes match the swing's natural frequency.

Period

The time that it takes a complete cycle to occur

A boat produces a wave as it passes an aluminum can floating in a lake. Explain why the can is not moved along in the direction of wave motion.

The water wave is a disturbance moving through the water, but water (the medium) is not carried forward with the wave.

How is the period of a simple harmonic vibration related to its frequency?

They are inversely related.

What is one advantage of transferring energy by electromagnetic waves?

They can transport energy through space (a vacuum).

Will the period of a vibrating mass-spring system on Earth be different from the period of an identical mass-spring system on the moon? Why or why not?

They will be the same because the period is independent of free-fall acceleration.

What is total internal reflection?

Total internal reflection can occur in situations when light attempts to travel from a material with a higher refractive index to one with a lower index of refraction. If the angle of incidence of the ray is greater than the critical angle, the ray is totally reflected at the boundary.

How do transverse and longitudinal waves differ?

Transverse wave particles vibrate perpendicular to wave motion. Longitudinal wave particles vibrate parallel to wave motion.

The brain interprets these impulses as...

sounds of varying frequencies.

Unlike a transverse wave on a rope, sound travels as a(n) ___ wave.

Unlike a transverse wave on a rope, sound travels as a(n) longitudinal wave. - Sound travels as a longitudinal wave because the molecules in the air vibrate in a direction that is parallel to the direction of the wave's motion.

Simple Harmonic Motion

Vibration about an equilibrium position in which a restoring force is proportional to the displacement from equilibrium

Although soldiers are usually required to march together in step, they must break their march when crossing a bridge. Explain the possible danger of crossing a rickety bridge without taking this precaution.

Vibrations could set the bridge in motion if they match one of the bridge's natural frequencies.

Sound Intensity

W/m² - watts/meters squared

How do wave speed, frequency, and wavelength relate to each other?

Wave speed equals frequency times wavelength.

A stretched string fixed at both ends is 2.0 m long. What are three wavelengths that will produce standing waves on this string? Name at least one wavelength that would not produce a standing wave pattern, and explain your answer.

Wavelengths that will produce standing waves include 4.0 m, 2.0 m, and 1.3 m; Any value that does not allow both ends of the string to be nodes is acceptable.

How does light from a laser differ from light whose waves all have the same wavelength but are not coherent?

Waves emitted by a laser do not shift relative to each other as time progresses (they are coherent and continuously in phase).

Which of the following is not an example of approximate simple harmonic motion? - a ball bouncing on the floor - a child swinging on a swing - a piano wire that has been struck - a car's radio antenna waving back and forth

a ball bouncing on the floor

A given difference in decibels corresponds to...

a fixed difference in perceived loudness.

The relationship between frequency, wavelength, and speed holds for light waves because

all forms of electromagnetic radiation travel at a single speed in a vacuum.

A vibrating string or a pipe open at both ends produces...

all harmonics.

The Doppler effect occurs with

all waves.

For a mass hanging from a spring, the maximum displacement the spring is stretched or compressed from its equilibrium position is the system's - amplitude - period - frequency - acceleration

amplitude

The angle between the string of a pendulum at its equilibrium position and at its maximum displacement is the pendulum's - period. - frequency. - vibration. - amplitude.

amplitude

The relative motion between the source of wave and an observer creates...

an apparent frequency shift known as the Doppler effect.

Two mechanical waves can occupy the same space at the same time because waves - are matter. - are displacements of matter. - do not cause interference patterns. - cannot pass through one another.

are displacements of matter.

Sound waves

are longitudinal waves.

Why does a pipe closed at one end have a different harmonic series than an open pipe?

because a closed end is a node, while an open end is an antinode

Why are sound waves in air characterized as longitudinal?

because air molecules vibrate in a direction parallel to the direction of wave motion

An ideal mass-spring system vibrating with simple harmonic motion would oscillate indefinitely. Explain why.

because frictional forces are neglected in an ideal mass-spring system

Why is the intensity of an echo less than that of the original sound?

because intensity decreases with distance and the sound has traveled from the source to a reflecting surface and back (and because of imperfect reflection)

Why do sound waves need a medium through which to travel?

because sound waves are vibrations of particles; Without particles, no propagation occurs.

Why is the threshold of hearing represented as a curve in Figure 9 (Section 2) rather than as a single point?

because the threshold of hearing depends on both frequency and intensity

Why do ultrasound waves produce images of objects inside the body more effectively than audible sound waves do?

because their short wavelengths can image small objects

What happens to the period of a simple pendulum when the pendulum's length is doubled? What happens when the suspended mass is doubled?

becomes √2 times as long; remains the same because mass does not affect period

Harmonic Series of Standing Waves on a Vibrating String

fn = n(v/2L); n = 1, 2, 3, ... - frequency = harmonic number × (speed of waves on the string)/(2)(length of vibrating string)

Harmonic Series of a Pipe Open at Both Ends

fn = n(v/2L); n = 1, 2, 3,... - frequency = harmonic number × (speed of sound in the pipe)/(2)(length of vibrating air column)

Harmonic Series of a Pipe Closed at One End

fn = n(v/4L); n = 1, 3, 5,... - frequency = harmonic number × (speed of sound in the pipe)/(4)(length of vibrating air column)

For a system in simple harmonic motion, which of the following is the number of cycles or vibrations per unit of time? a. amplitude b. period c. frequency d. revolution

frequency

April is about to release the bob of a pendulum. Before she lets go, what sort of potential energy does the bob have? How does the energy of the bob change as its swings through one full cycle of motion?

gravitational potential energy; When April lets go of the bob, PE = max and KE = 0. At the bottom of its swing, KE = max and PE = 0.

A bat flying toward a wall emits a chirp at 40 kHz. Is the frequency of the echo received by the bat greater than, less than, or equal to 40 kHz?

greater than 40 kHz

A train moves down the track toward an observer. The sound from the train, as heard by the observer, is ___ the sound heard by a passenger on the train.

higher in pitch than

Suppose you hear music being played from a trumpet that is across the room from you. Compressions and rarefactions from the sound wave reach your ear, and you interpret these vibrations as sound. Were the air particles that are vibrating near your ear carried across the room by the sound wave? How do you know?

no; As with all waves, the disturbance travels, not the material itself. Individual air molecules do not move across the room with the sound wave. Instead, each molecule vibrates in place, and the vibrations are transferred from one particle to the next.

If a 15-person musical ensemble gains 15 new members, so that its size doubles, will a listener perceive the music created by the ensemble to be twice as loud? Why or why not?

no; The intensity doubles, but loudness is not directly proportional to intensity.

The process of stimulated emission involves producing a second wave that is identical to the first. Does this gaining of a second wave violate the principle of energy conservation? Explain your answer.

no; The second light wave is obtained from the energy that is added to an atom in the active medium by an external energy source.

Could a portion of the innermost wave front shown in Figure 6 be approximated by a plane wave? Why or why not?

no; The wave front must be far from the source (relative to the wavelength) to be approximated by plane waves.

If a pendulum clock keeps perfect time at the base of a mountain, will it also keep perfect time when moved to the top of the mountain? Explain.

no; ag would change slightly, so T would also change.

The motion of Earth orbiting the sun is periodic. Is this motion simple harmonic? Why or why not?

no; because Earth does not oscillate about an equilibrium position

Audible beats are formed by the interference of two waves

of slightly different frequencies.

How far does a wave travel in one period?

one wavelength

At a distance of 3 m, the intensity of a sound will be ___ the intensity it was at a distance of 1 m.

one-ninth

A pipe closed at one end produces...

only odd harmonics.

What characterizes an object's motion as simple harmonic?

oscillation about an equilibrium position in which a restoring force is proportional to displacement

For a system in simple harmonic motion, which of the following is the time required to complete a cycle of motion? - amplitude - period - frequency - revolution

period

One end of a taut rope is fixed to a post. What type of wave is produced if the free end is quickly raised and lowered one time? - pulse wave - periodic wave - sine wave - longitudinal wave

pulse wave

Which best describes the image of a concave mirror when the object is at a distance greater than twice the focal point distance from the mirror?

real, inverted, and magnification less than one

Waves arriving at a fixed boundary are - neither reflected nor inverted. - reflected but not inverted. - reflected and inverted. - inverted but not reflected.

reflected and inverted.

Decibel level is a measure of...

relative intensity on a logarithmic scale.

When the frequency of a force applied to a system matches the natural frequency of vibration of the system, ___ occurs.

resonance

A force vibration at the natural frequency produces...

resonance.

In general, sound travels faster through

solids than through gases.

Give three examples of mechanical waves. How are these different from electromagnetic waves, such as light waves?

sound waves, water waves, and waves on a spring; Light waves do not need a medium to move through, but mechanical waves do.

A simple pendulum swings in simple harmonic motion. At maximum displacement, - the acceleration reaches a maximum. - the velocity reaches a maximum. - the acceleration reaches zero. - the restoring force reaches zero.

the acceleration reaches a maximum.

A fire engine is moving at 40 m/s and sounding its horn. A car in front of the fire engine is moving at 30 m/s, and a van in front of the car is stationary. Which observer hears the fire engine's horn at a higher pitch, the driver of the car or the driver of the van?

the driver of the van

Harmonics are integral multiples of...

the fundamental frequency.

What is the fundamental frequency? How are harmonics related to the fundamental frequency?

the lowest possible frequency of a vibrating system; They are integral multiples of the fundamental frequency.

Which of the following most affects the wavelength of a mechanical wave moving through a medium? Assume that the frequency of the wave remains constant. - the nature of the medium - the amplitude - the height of a crest - the energy carried by the wave

the nature of the medium

The sound intensity of a spherical wave is...

the power per area.

Which of the following features of a given pendulum changes when the pendulum is moved from Earth's surface to the moon? - the mass - the length - the equilibrium position - the restoring force

the restoring force

Flat mirrors form virtual images that are ___ distance from the mirror's surface.

the same

Sound intensity is inversely proportional to the square of the distance from the source because...

the same energy is spread over a larger area.

Standing waves are produced by periodic waves of

the same frequency, amplitude, and wavelength traveling in opposite directions.

The number and intensity of harmonics account for...

the sound quality of an instrument, also known as timbre.

When two mechanical waves coincide, the amplitude of the resultant wave is always ___ the amplitudes of each wave alone. - greater than - less than - the sum of - the same as

the sum of

In a simple pendulum, the weight of the bob can be divided into two components, one tangent to the bob's direction of motion and the other perpendicular to the bob's direction of motion. Which of these is the restoring force, and why?

the tangent component; because it always pulls the bob toward the equilibrium position

If a spring is stretched from a displacement of 10 cm to a displacement of 30 cm, the force exerted by the spring increases by a factor of

three

What is the purpose of the slide on a trombone and the valves on a trumpet?

to change the length of the air column, thereby changing the fundamental frequency

If the source of the waves in Figure 7 is stationary, which way must the ripple tank be moving?

to the left

Figure 7 is a diagram of the Doppler effect in a ripple tank. In which direction is the source of these ripple waves moving?

to the right

A wave travels through a medium. As the wave passes, the particles of the medium vibrate in a direction perpendicular to the direction of the wave's motion. The wave is - longitudinal - a pulse - electromagnetic - transverse

transverse

Under what conditions does resonance occur?

when a forced vibration is the same as the natural frequency of a vibrating system

Intensity and frequency determine...

which sounds are audible.

Can more than two waves interfere in a given medium?

yes, because waves do not collide like other matter; They add to form a resultant wave.

A student records the first 10 harmonics for a pipe. Is it possible to determine whether the pipe is open or closed by comparing the difference in frequencies between the adjacent harmonics with the fundamental frequency? Explain.

yes; This difference will equal the fundamental frequency if the pipe is open at both ends but will equal twice the fundamental frequency if the pipe is closed at one end.

When two waves interfere, can the resultant wave be larger than either of the two original waves? If so, under what conditions?

yes; when constructive interference occurs

What is the resultant displacement at a position where destructive interference is complete?

zero