Physical Science - Chapter 5 - Wave Motions and Sound

There is a direct relationship between the extent of stretching or compression of a spring and the amount of force applied to it. A large force stretches a spring a lot; a small force stretches it a little. As long as the applied force does not exceed the elastic limit of the spring, the spring will always return to its original shape when you remove the applied force. There are three important considerations about the applied force and the response of the spring:

1) The greater the applied force, the greater the compression or stretch of the spring from its original shape. 2) The spring appears to have an internal restoring force, which returns it to its original shape. 3) The farther the spring is pushed or pulled, the stronger the restoring force that returns the spring to its original shape.

A motion of vibrating mass is described by measuring three basic quantities called the:

1) amplitude of vibration 2) the period 3) the frequency of vibration

The nature of the molecules making up a solid, liquid, or gas determines how well or how rapidly the substance will carry sound waves. The two variables are:

1) the inertia of the molecules 2) the strength of the interaction.

Cycle

A complete vibration is called a cycle. A cycle is the movement from some point, say the far left, all the way to the far right and back to the same point again, the far left in this example.

When a wave front strikes a boundary that is parallel to the front, the wave may be absorbed, be transmitted, or undergo a change in direction, depending upon the nature of the boundary. When waves undergo a change in direction, or reflection, they can bounce directly back, or they can be deflected off at an angle.

Also depending upon the nature of the boundary, the wave may be partly absorbed, partly transmitted, partly reflected, or any combination of these things. Some materials, such as hard, smooth surfaces, reflect sound waves more than they absorb them. Other materials, such as soft, ruffly curtains, absorb sound waves more than they reflect them. If you have ever been in a room with smooth, hard walls and no curtains, carpets, or furniture, you know that sound waves may be reflected several times before they are finally absorbed.

Match the term used to describe a vibration to its definition.

Amplitude ---- > The largest displacement from the equilibrium position ------ > The number of seconds per cycle Frequency -----> The number of cycles per second

rarefaction

An area where the particles in a medium are spread out. A pulse of thinned-out molecules.

Resonance

An external force with a frequency that matches the natural frequency of an object results in resonance. When the two frequencies match, energy is transferred very efficiently. This condition, when the frequency of an external force matches the natural frequency, is called resonance.

An echo is heard exactly 1.00 s after a sound when the speed of sound is 1,147 ft/s. How many feet away is the reflecting surface?

Answer = 1,147ft X 1/2 = 574 ft

The air temperature is 86.0 degrees F. What is the velocity of sound in ft/s? (Note that degrees F must be converted to degrees C. )

Answer = Tc = 1147 ft/s

A complete vibration occurs with a motion away from a point, to the other side of the equilibrium position, and back again to the starting point; this complete vibration is called a ______.

Cycle

Material that is capable of recovering its shape after a force deforms it is called _________ .

Elastic

If a mass is attached to a spring but the spring is not applying a force to the mass, then the spring is in its ______ position.

Equilibrium Reason: At the equilibrium position, the spring is not compressed or stretched.

true or false: Mammals (humans, dolphins, dogs, bats, etc.) all can hear in just about the same range of frequencies.

False

The unit of measurement for frequency is the ________ .

Hertz (Hz)

Match the terms for longitudinal sound waves to their frequencies in hertz (Hz).

Infrasonic -------> Less than 20 Hz Audible -----> Between 20 and 20,000 Hz Ultrasonic ----- > Over 20,000 Hz

The intensity of a sound wave is a measure of the energy the sound wave is carrying (Figure 5.18). Intensity is defined as the power (in watts) transmitted by a wave to a unit area (in square meters) that is perpendicular to the waves.

Intensity is therefore measured in watts per square meter (W/m^2) or intensity = power/area 1 = P/A

Refraction

Light moving from one transparent material to another undergoes a change of direction called refraction. The bending of a wave front at boundaries is called refraction. Refraction changes the direction of travel of a wave front.

Which of the following statements is true in regard to hearing within the animal kingdom?

Many nonhuman animals can hear sounds outside of the ranges that humans can hear.

Waves

Mechanical waves are longitudinal or transverse. In reference to a pebble being dropped in a pond, the disturbance sets the molecules of the water medium in motion, in periodic vibrations. As vibrations travel across the medium we see patterns that we call waves.

There is a relationship between the wavelength, period, and speed of a wave.

Recall that speed is v = distance/time Since it takes one period (T) for a wave to move one wavelength (λ), then the speed of a wave can be measured from v = one wavelength/one period = λ/T The frequency, however, is more convenient than the period for dealing with waves that repeat themselves rapidly. Recall that the relationship between frequency (f) and the period (T) is f = 1/T Substituting f for 1/T yields v = λf This equation tells you that the velocity of a wave can be obtained from the product of the wavelength and the frequency. Note that it also tells you that the wavelength and frequency are inversely proportional at a given velocity.

The continuation of many reflections causes a tone to gain in volume. Such mixing of reflected sounds with the original is called reverberation.

Reverberation adds to the volume of a tone, and it is one of the factors that determine the acoustical qualities of a room, lecture hall, or auditorium.

Humans do not hear infrasonic or ultrasonic sounds, but various animals have different limits. Dogs, cats, rats, and bats can hear higher frequencies than humans. Dogs can hear an ultrasonic whistle when a human hears nothing, for example.

Some bats make and hear sounds of frequencies up to 100,000 Hz as they navigate and search for flying insects in total darkness. Scientists discovered recently that elephants communicate with extremely low-frequency sounds over distances of several kilometers. Humans cannot detect such low-frequency sounds. This raises the possibility of infrasonic waves that other animals can detect that we cannot.

Which statement below reflects the relative speed of travel of sound and light waves in air?

Sound waves are slower than light waves.

audible sound waves

Sound waves that the average human ear can hear (20 to 20 000 Hz)

Light travels so rapidly that you can consider what you see to be simultaneous with what is actually happening for all practical purposes.

Sound, however, travels much more slowly, and the sounds arrive late in comparison to what you are seeing. This is dramatically illustrated by seeing a flash of lightning, then hearing thunder seconds later.

A vibrating system has a period of 0.5s. What is the frequency in Hz?

T = 0.5s f = ? f = 1/T f = 1/0.5s f = 1/0.5 1/s f = 2 1/s f = 2 Hz

The period and frequency are two ways of describing the time involved in a vibration. Since the period (T) is the number Page 119of seconds per cycle and the frequency (f) is the number of cycles per second, the relationship is

T = 1/f or f = 1/T

Reflection

The law of reflection states that the angle of an incoming ray of light and the angle of the reflected light are always equal.

The human ear can distinguish a reflected sound pulse from the original sound pulse if 0.10 s or more elapses between the two sounds. What is the minimum distance to a reflecting surface from which we can hear an echo if the speed of sound is 343 m/s?

The minimum distance to a reflecting surface from which we hear an echo when the air is at room temperature is therefore 17 m (about 56 ft)

Resonant Frequency

The natural frequency of an object is thus referred to as the resonant frequency, that is, the frequency at which resonance occurs.

When an object moves through the air at the speed of sound, it keeps up with its own sound waves. All the successive wave fronts pile up on one another, creating a large wave disturbance called a shock wave.

The shock wave from a supersonic airplane is a cone-shaped shock wave of intense condensations trailing backward at an angle dependent on the speed of the aircraft.

Sound waves, however, move in three-dimensional space like a rapidly expanding balloon. The source of the sound is normally in the center of these spherical waves.

The waves themselves exist as outwardly moving areas in which the medium's molecules are compressed together (condensations), alternating with outwardly moving areas in which the medium's molecules are not compressed and are less dense (rarefractions). The crest of each condensation zone can be considered a wave front. The distance from one wave front to the next identifies one complete wave or wavelength. While close to the source of the sound, these wave fronts appear to be curved. At some distance from the source, each wave has become sufficiently large that a small part of a spherical wave front appears to be flat, and it can be considered a linear wave front.

All sounds have a vibrating object as their source. The vibrations of the object send pulses or waves of condensations and rarefactions through the air.

These sound waves have physical properties that can be measured, such as frequency and intensity.

If a reflected sound arrives after 0.10 s, the human ear can distinguish the reflected sound from the original sound. A reflected sound that can be distinguished from the original is called an echo.

Thus, a reflected sound that arrives before 0.10 s is perceived as an increase in volume and is called a reverberation, but a sound that arrives after 0.10 s is perceived as an echo.

Hertz (Hz)

Unit of measurement for frequency. Frequency is measured in a unit called a hertz (Hz). The unit for a hertz is 1/s since a cycle does not have dimensions. Thus, a frequency of 10 cycles per second is referred to as 10 hertz or 10 1/s. In other words, frequency (f) tells you how many full vibrations (or full cycles) are performed in 1 second.

What is the velocity of sound in m/s at room temperature (20.0 degrees C)?

V0 = 331 m/s Tp = 20.0 degrees C VTp = ? VTp = ( 0.600 m/s// degrees C) (Tp) VTp = 331 m/s + (0.600 m/s// degrees C) (20.0 degrees C) VTp = 331 m/s + (0.600 X 20.0) m/s// degrees C X degrees C VTp = 331 m/s + 12.0 m/s VTp = 343 m/s

The simple relationship of the speed of sound at 0 degrees Celsius plus the fractional increase per degree above 0 degrees Celsius can be combined as in the following equations:

VTP (m/s) = V0 + (0.600 m/s//C degrees )(Tp) where VTp is the velocity of sound at the present temperature, V0 is the velocity of sound at 0 degrees Celsius, and Tp is the present temperature. This equation tells you that the velocity of a sound wave increases 0.6 m/s for each degree Celsius above 0 degrees Celsius. For units of ft/s, VTp (ft/s) = V0 + (2.00 ft/s// degree C) (Tp) The velocity of a sound wave increases 2.0 ft/s for each degree Celsius above 0 degree C.

A back-and-forth motion that repeats itself is called a(n) ______.

Vibration

Match the wave terminology to its description.

Wave Crest ----- > The maximum disturbance from the undisturbed (rest) position. Wave Trough ----- > The maximum disturbance in the opposite direction from the rest position. Amplitude ----- > The maximum displacement from the rest position.

Match the following terms used to characterize waves to their descriptions.

Wavelength -----> The distance between two identical points on adjacent waves Period -----> The amount of time for a wave to repeat itself Rest Position -----> The place any undisturbed molecules would be located.

Equilibrium position

When the mass has not been disturbed, it is at rest at an equilibrium position. At the equilibrium position, the spring is not compressed or stretched, so it applies no force on the mass. Note: At Equilibrium position the force is zero. Example: A see-saw at a park is balanced equally on both sides when its at rest and no one is on it. Simple terms: Think of it as the "happy spot" where the object feels most comfortable. If you disturb it, it wants to return there.

Vibration

a back-and-forth motion that repeats itself. A motion that repeats itself is called periodic motion.

Standing Wave

a condition where two waves of equal frequency traveling in opposite directions meet and form stationary regions of maximum displacement due to constructive interference and stationary regions of zero displacement due to destructive interference. This pattern of alternating nodes and antinodes does not move along the string and is thus called a standing wave. Note that standing wave for one wavelength will have a node at both ends and in the center and also two antinodes. Standing waves occur at the natural, or resonant, frequencies of the string, which are a consequence of the nature of the string, the string length, and the tension in the string. Since the standing waves are resonant vibrations, they continue as all other waves quickly fade away.

Longitudinal waves cause vibrations to occur in Blank______.

a direction parallel to their own movement

Longitudinal waves cause vibrations to occur in ________.

a direction parallel to their own movement.

sinusoidal

a graph or a function that has the form of a sine or cosine function.

Shock Wave

a large, intense wave disturbance of very high pressure -- for example, the pressure wave created by an explosion.

Longitudinal Wave

a mechanical disturbance that causes particles to move closer together and farther apart in the same direction that the wave is traveling.

Transverse Wave

a mechanical disturbance that causes particles to move perpendicular to the direction that the wave is traveling. You will make a different kind of mechanical wave in the stretched spring if you now move your hand up and down. This motion creates a transverse wave. A transverse wave is a disturbance that causes motion perpendicular to the direction that the wave is moving. Particles responding to a transverse wave do not move closer together or farther apart in response to the disturbance; rather, they vibrate up and then down in a direction perpendicular to the direction of the wave motion.

Echo

a reflected sound that can be distinguished from the original sound, which usually arrives 0.1s or more after the original sound.

Sound is transmitted in air as longitudinal waves because Blank______.

air molecules are not attached to one another and therefore cannot transmit transverse waves

Doppler Effect

an apparent shift in the frequency of sound or light due to relative motion between the source of the sound or light and the observer. The overall effect of a higher pitch as a source approaches and then a lower pitch as it moves away is called the Doppler effect. The Doppler effect is evident if you stand by a street and an approaching car sounds its horn as it drives by you. You will hear a higher-pitched horn as the car approaches, which shifts to a lower-pitched horn as the waves go by you. The driver of the car, however, will hear the continual, true pitch of the horn because the driver is moving with the source.

Periodic motion

any motion that repeats at regular time intervals. Vibration is an example of periodic motion. Such a motion is not restricted to any particular direction, and it can be in many different directions at the same time. Almost any solid can be made to vibrate if it is elastic.

Reverberation

apparent increase in volume caused by reflections, usually arriving within 0.1 second after the original sound. An open-air concert sounds flat without the reverberation of an auditorium and is usually enhanced electronically to make up for the lack of reflected sounds. Too much reverberation in a room or classroom is not good because the spoken word is not as sharp. Sound-absorbing materials are therefore used on the walls and floors where clear, distinct speech is important. The carpet and drapes you see in a movie theater are not decorator items but are there to absorb sounds.

The equilibrium position is where a spring is ______.

at rest and not applying a force to an attached mass.

The equilibrium position is where a spring is __________.

at rest and not applying a force to an attached mass.

A vibration is a ______.

back-and-forth motion that repeats itself

You cannot hear a vibrating door because the human ear normally hears sounds originating from vibrating objects with a frequency

between 20 and 20,000 Hz. Longitudinal waves with frequencies less than 20 Hz are called infrasonic. You usually feel sounds below 20 Hz rather than hear them, particularly if you are listening to a good sound system. Longitudinal waves above 20,000 Hz are called ultrasonic.

When waves encounter different conditions, such as a change in the temperature, humidity, or nature of the material, a division referred to as a(n) ________ forms.

boundary

A material is elastic if it ______.

can recover its shape after a force deforms it.

In general, the human ear is most sensitive to sounds at 2,500 Hz. Assuming that sound moves at 330 m/s, what is the wavelength of sounds to which people are most sensitive?

f = 2,500 Hz v = 330 m/s λ = ? v = λf λ = v/f λ = 330m/s//2500 1/s λ = 330/2500 λ = 0.13m or 13cm

A sound wave with a frequency of 260 Hz has a wavelength of 1.27 m. With what speed would you expect this sound wave to move?

f = 260 Hz λ = 1.27 m v = ? v = λf v = (1.27 m) (260 1/s) v = 1.27 x 260m X 1/s v = 330 m/s

The hertz (Hz) is a measurement of ______, and one hertz is expressed in units of 1/s.

frequency

When two traveling waves meet, they can interfere with each other, producing a new disturbance. This new disturbance has a different amplitude, which is the sum of the amplitudes of the two original wave patterns. If the wave crests or wave troughs arrive at the same place at the same time, the two waves are said to be

in phase, and the two amplitudes are positively added together. The new disturbance has a crest and trough that has greater displacement than either of the two separate waves. This is called constructive interference (Figure 5.16A). If the trough of one wave arrives at the same place and time as the crest of another wave, the waves are completely out of phase. The crest of one wave (positive displacement) will cancel the trough of the other wave (negative displacement), and the result is zero total disturbance, or no wave. This is called destructive interference (Figure 5.16B).

The amplitude of a wave

is the maximum displacement from rest to the crest or from rest to the trough.

The wave crest

is the maximum disturbance from the undisturbed (rest) position. For a sound wave, this would represent the maximum increase of air pressure.

The wave trough

is the maximum disturbance in the opposite direction from the rest position. For a sound wave, this would represent the maximum decrease of air pressure.

Period (T) or Wave

is the number of seconds per cycle. For example, suppose 0.1 s is required for an object to move through one complete cycle, to complete the motion from one point, then back to that point. The period of this vibration is 0.1 s. In other words, the period T is the time of one full cycle or one full vibration.

A disturbance that causes particles to move closer together or farther apart in the same direction that the wave is moving is a Blank______ wave.

longitudinal

Sound waves in air must be _________ waves since air molecules are not attached to their neighboring molecules.

longitudinal

Because air is fluid, mechanical waves in air can only be

longitudinal; therefore, sound waves in air must be longitudinal.

The wavelength is the distance from a part of one wave to the same part in the next wave, such as from one crest to the next. The amplitude is the

maximum distance above or below the resting equilibrium position. The cycle period is the time required for a wave to repeat itself, that is, the time for one complete wavelength to move past a given location.

Wavelengths are measured in Blank______ and denoted by the Greek letter λ.

meters

A cycle is ________.

one complete vibration.

In a vibration, the number of seconds per cycle is called the ________, and the number of cycles per second is the ____________.

period , frequency

A transverse wave causes a disturbance Blank______.

perpendicular to the direction of its travel

An elastic material is one that is capable of

recovering its shape after a force deforms it.

Sonic Boom

sound waves that pile up into a shock wave when a source is traveling at or faster than the speed of sound.

Ultrasonic

sound waves too high in frequency to be heard by the human ear; frequencies above 20,000 Hz.

Infrasonic

sound waves too low a frequency to be heard by the human ear; sound having a frequency of less than 20 Hz.

Traveling vibrations in a medium are better known as _______.

sound.

At a great enough distance from a source, a small part of a Blank______ wave can be considered a Blank______ wave front.

spherical; linear

A quantity called the wavelength of a wave can be measured as

the distance between either two adjacent crests or two adjacent troughs, or any two identical points of adjacent waves. The wavelength is denoted by the Greek Letter λ (pronounced "lambda") and is measured in meters.

Amplitude or amplitude of vibration

the extent of displacement from the equilibrium condition; the size of a wave from the rest (equilibrium) position. The amplitude is the largest displacement from the equilibrium position (rest position) that the mass can have in this motion. All other displacements that you may see and measure, when observing a vibrating mass, are smaller than the amplitude.

pitch

the frequency of a sound wave.

Wavelength

the horizontal distance between successive wave crests or other successive parts of the wave.

Fundamental Frequency

the lowest frequency (longest wavelength) that can set up standing waves in an air column or on a string.

Frequency (f)

the number of cycles of a vibration or of a wave occurring in 1 second, measured in units of cycles per second (hertz). The number of cycles per second. For example, a vibrating object moves through 10 cycles in 1 s. The frequency of this vibration is 10 cycles per second. Frequency is measured in a unit called a hertz (Hz).

Simple harmonic motion

the vibratory motion that occurs when there is a restoring net force opposite to and proportional to a displacement. Simpler terms: It is a repetitive movement where an object oscillates around an equilibrium position. Oscillate - move or swing back and forth at a regular speed.

A wave that causes a disturbance perpendicular to the direction of its travel is a(n) _________ wave.

transverse

Mechanical waves are Blank______.

traveling vibrations in a medium

Mechanical waves are _______.

traveling vibrations in a medium Reason: Mechanical waves cannot travel without a medium.

Sound waves with frequencies greater than 20,000 Hz are known as Blank______, whereas those with frequencies of less than 20 Hz are known as Blank______.

ultrasonic; infrasonic

A cycle is one complete

vibration. The period is the number of seconds per cycle. The frequency is a count of how many cycles are completed in 1 second.

The symbol for wave length is __________.

λ

When a wave encounters a different condition (temperature, humidity, or nature of material), however, drastic changes may occur rapidly. The division between two physical conditions is called a boundary. Boundaries are usually encountered

(1) between different materials or (2) between the same materials with different conditions.

The loudness of a sound is a subjective interpretation that varies from person to person. Loudness is also related to

(1) the energy of a vibrating object, (2) the condition of the air that the sound wave travels through, and (3) the distance between you and the vibrating source. Furthermore, doubling the amplitude of the vibrating source will quadruple the intensity of the resulting sound wave, but the sound will not be perceived as four times as loud. The relationship between perceived loudness and Page 129the intensity of a sound wave is not a linear relationship. In fact, a sound that is perceived as twice as loud requires 10 times the intensity, and quadrupling the loudness requires a 100-fold increase in intensity.

Before we consider these resonant patterns in detail, keep in mind that:

(1) two or more waves can be in the same place at the same time, traveling through one another from opposite directions; (2) a confined wave will be reflected at a boundary, and the reflected wave will be inverted (a crest becomes a trough); and (3) reflected waves interfere with incoming waves of the same frequency to produce standing waves.

Select the two factors below that determine how well a substance can carry a sound wave.

- The inertia of the molecules. - The strength of the interaction between molecules.