Chapter 19 Vibrations and Waves

What happens to the wavelength of a wave when the frequency decreases?

(If the speed is constant) the wavelength increases as the frequency decreases.

How many nodes, not including the endpoints, are there in a standing wave that is two wavelengths long? Three wavelengths long?

2-1 3-2

If a train of freight cars, each 10 m long, rolls by you at the rate of three cars each second, what is the speed of the train?

30 m/s. We can see this in two ways: a. According to the definition of speed from Chapter 2, v = d/t = (3 x 10 m)/1 s = 30 m/s, since 30 m of train passes you in 1 s. b. If we compare our train to wave motion, where wavelength corresponds to 10 m and frequency is 3 Hz, then speed = frequency x wavelength = 3 Hz x 10 m = 3/s x 10 m = 30 m/s (Note that 3 Hz is 3 cycles in 1 s, or simply 3/s, because cycles, just a count, needn't be written in the unit for frequency.)

What kind of motion should you impart to the nozzle of a garden hose so that the resulting stream of water approximates a sine curve?

up and down

Red light has a longer wavelength than violet light. Which has the higher frequency?

violet light has the higher frequency

If a gas tap is turned on for a few seconds, someone a couple of meters away will hear the gas escaping long before she smells it. What does this indicate about the speed of sound and the speed at which molecules diffuse through the sound-carrying medium?

when a gas tap is turned on it indicated that sound of the gas tap travels in air but just transferring the energy from one molecule to the another on the other hand we hear the smell after sometime because smell travels by the actual moment of air so it takes a sometime for we to get the smell. -(sic) Yahoo Answers

How fast does a supersonic aircraft fly compared with the speed of sound?

faster than the speed of sound

True or false: In order for an object to produce a sonic boom, it must be "noisy." Give two examples to support your answer.

*False* It is not necessary that the moving source be "noisy" to produce a shock wave. Once an object is moving faster than the speed of sound, it will make a sound.

True or false: A sonic boom occurs only when an aircraft is breaking through the sound barrier. Defend your answer.

*False* The aircraft may have exceeded the speed of sound earlier.

Does a sonic boom occur at the moment when an aircraft exceeds the speed of sound? Explain.

A shock wave and the resulting sonic boom are produced whenever an aircraft is supersonic, whether or not the aircraft had just become supersonic or has been supersonic for hours.

If a pendulum is shortened, does its frequency increase or decrease? What about its period?

A shorter pendulum swings to and fro with a higher frequency and shorter period

How does a sine curve relate to the wave description?

A sine curve is a pictorial representation of a wave.

Standing wave

A stationary interference pattern formed in a medium when two sets of identical waves pass through the medium in opposite directions.

A bow wave on the surface of water is two-dimensional. How about a shock wave in air?

A supersonic aircraft generates a three-dimensional shock wave. Just as a bow wave is produced by overlapping circles that form a V, a shock wave is produced by overlapping spheres that form a cone.

Longitudinal wave

A wave in which the medium vibrates parallel to (along) the direction in which the wave travels. Sound waves are longitudinal.

Transverse wave

A wave in which the medium vibrates perpendicularly (at right angles) to the direction in which the wave travels. Light waves and waves on stringed instruments are transverse.

What is a wiggle in time called? What do you call a wiggle in space and time?

A wiggle in time is a vibration: a wiggle in space and time is a wave

If the frequency of a particular wave is 20 Hz, its period is A.1/20 second. B.20 seconds. C.more than 20 seconds. D.None of the above.

A. 1/20 second. Explanation:Note when ƒ = 20 Hz, T = 1/ƒ = 1/(20 Hz) = 1/20 second.

What kinds of waves can show interference?

All waves can show interference.

You pick up an empty briefcase and let it swing to and fro at its natural frequency. If the case were filled with books, would the natural frequency be lower than, higher than, or the same as before?

Assuming the center of gravity of the suitcase doesn't change when loaded with books, the pendulum rate of the empty case and the loaded case would be the same. This is because the period of a pendulum is independent of mass. Since the length of the pendulum doesn't change, the frequency and hence the period would be unchanged.

A banjo player plucks the middle of a string pinned down at both ends. Where are the nodes of the standing wave in the string? What is the wavelength of the vibrating string?

At the ends of the string, twice as long as the string.

Why is there a Doppler effect when the source of the sound is stationary and the listener is in motion? In which direction should the listener move to hear a higher frequency? A lower frequency?

Because the Doppler effect is when a shift in the frequency due to motion. To hear a higher frequency you should be going toward the stationary sound source. To hear a lower frequency you should be moving away from the sound source.

Why is it that a subsonic aircraft, no matter how loud it may be, cannot produce a sonic boom?

Because the sound waves that reach our ears are perceived as one continuous tone.

The distance between adjacent peaks in the direction of travel for a transverse wave is its A.frequency. B.period. C.wavelength. D.amplitude.

C. wavelength. Explanation:The wavelength of a transverse wave is also the distance between adjacent troughs, or between any adjacent identical parts of the waveform.

How do frequency and period relate to each other?

Frequency (vibrations per second) and period (seconds per vibration) are reciprocals *Frequency = 1/period* and *Period = 1/frequency*

A bat chirps as it flies toward a wall. Is the frequency of the echoed chirps it receives higher than, lower than, or the same as the emitted ones?

Higher

Suppose you set up a standing wave of three segments, as shown in Figure 19.13c. If you shake with twice as much frequency, how many wave segments will occur in your new standing wave? How many wavelengths?

If you impart twice the frequency to the rope, you'll produce a standing wave with twice as many segments, so you'll have six segments. Since a full wavelength has two segments, you'll have three complete wavelengths in your standing wave.

In what direction are the vibrations relative to the direction of wave travel in a transverse wave?

In a transverse wave, vibrations are perpendicular to the direction of wave travel.

A grandfather pendulum clock keeps perfect time. Then it is relocated to a summer home high in the mountains. Does it run faster, slower, or the same? Explain.

In addition to length, the period of a pendulum depends on the acceleration due to gravity. Oil and mineral prospectors use very sensitive pendulums to detect slight differences in this acceleration, which is affected by the densities of underlying formations. *Slower because if the acceleration due to gravity is lower, then the period will increase, which means the time it takes will be longer/slower.*

In one word, what is it that moves from source to receiver in wave motion?

Energy moves from source to receiver.

Frequency

For a vibrating body or medium, the number of vibrations per unit time. For a wave, the number of crests that pass a particular point per unit time.

Amplitude

For a wave or vibration, the maximum displacement on either side of the equilibrium (midpoint) position.

What is the source of mechanical waves? Of electromagnetic waves?

For mechanical waves, the source is something that vibrates. For electromagnetic waves, the source is vibrating electric charges.

If the speed of a wave doubles while the wavelength remains the same, what happens to the frequency?

It doubles.

Would it be correct to say that the Doppler effect is the apparent change in the speed of a wave due to motion of source? (Why is this question a test of reading comprehension as well as a test of physics knowledge?)

It is correct.

What can you say about the speed of a boat that makes a bow wave?

It is going faster than the wave speed.

You use a vice to firmly clamp one end of a hacksaw blade. You twang the free end and it vibrates. If you do the same, but first place a wad of clay on the free end, how, if at all, will the frequency of the vibration differ? Would it make a difference if the wad of clay were stuck to the middle? Explain. (Why could this question have been asked back in Chapter 8?)

It will make the period of vibration of the system longer because you have increased the moment of inertia of the system. If you put the clay in the middle then it won't be as longer.

Discuss how some learners confuse the two terms *wave speed* and *wave frequency* when they assume that the terms refer to the same thing.

It's important to note that wave speed involves the rate of travel while wave frequency involves how frequently vibration occurs

If we double the frequency of a vibrating object or the wave it produces, what happens to the period?

Lessens

In what direction are the vibrations relative to the direction of wave travel in a longitudinal wave?

Motion is along the direction of the wave rather than at right angles to it.

While you're at rest, a sound source moves toward you. Do you measure the speed of its sound wave to be greater or less than if the source were stationary?

Neither! Both the frequency and the wavelength undergo a change when the source is moving, but the wave speed does not. Be clear about the distinction between frequency and speed.

Is there an appreciable Doppler effect when the motion of the source is at right angles to a listener? Explain.

No there is no Doppler effect in the perpendicular direction.

Does the period of a pendulum depend on the mass of the bob? On the length of the string?

No, the period does not depend on the mass. It depends on the length, but not the amplitude, it also depends on gravity

When you blow your horn while driving toward a stationary listener, the listener hears an increase in the frequency of the horn. Would the listener hear an increase in the horn frequency if he or she were also in a car traveling at the same speed in the same direction as your are? Explain.

No. The effects of shortened waves and stretched waves would cancel one another.

What is a node? What is an antinode?

Nodes are the regions of minimal or zero displacement, with minimal or zero energy.•Antinodes are the regions of maximum displacement and maximum energy.•Antinodes and nodes occur equally apart from each other.

How does the Doppler effect aid police in detecting speeding motorists?

Police use radar waves that are reflected from moving cars. From the shift in the returned frequencies, the speed of the reflectors (car bodies) is determined.

Is the time required to swing to and fro (the period) on a playground swing longer or shorter when you stand rather than sit? Explain

Shorter because the center of gravity is higher and closer to the pendulum swing

Can standing waves be formed of transverse waves, longitudinal waves, or both?

Standing waves can be formed of both transverse and longitudinal waves.

What is meant by a blue shift and a red shift for light?

The Doppler effect also occurs for light. When a light source approaches, there is an increase in its measured frequency; when it recedes, there is a decrease in its frequency. An increase in frequency is called a blue shift because the increase is toward the high-frequency (or blue) end of the color spectrum. A decrease in frequency is called a red shift, referring to a shift toward the lower-frequency (or red) end of the color spectrum.

Can the Doppler effect be observed with longitudinal waves, with transverse waves, or with both?

The Doppler effect can be observed with both transverse and longitudinal waves.

Hertz

The SI unit of frequency. One hertz (symbol Hz) equals one vibration per second.

Bow wave

The V-shaped disturbance created by an object moving across a liquid surface at a speed greater than the wave speed

How does the phenomenon of interference play a role in the production of bow waves or shock waves?

The bow or shock wave is actually the superposition of many lower-amplitude waves that interfere constructively. When the crest of one wave overlaps the crest of another, and then another, a wave of higher amplitude is produced.

What is simple harmonic motion? Mention suitable examples.

The condition for simple harmonic motion is that the restoring force is proportional to the displacement from equilibrium. This condition is met, at least approximately, for most vibrations. The component of weight that restores a displaced pendulum to its equilibrium position is directly proportional to the pendulum's displacement (for small angles)----likewise for a bob attached to a spring. Recall, from Chapter 12, that Hooke's law for a spring is F = k(change in x,) where the force to stretch (or compress) a spring is directly proportional to the distance stretched (or compressed).

Shock wave

The cone-shaped disturbance created by an object moving at supersonic speed through a fluid.

Wavelength

The distance between successive crests, troughs, or identical parts of a wave.

A rock is dropped in water, and waves spread over the flat surface of the water. What becomes of the energy in these waves when they die out?

The energy of a water wave spreads along the increasing circumference of the wave until its magnitude diminishes to a value that cannot be distinguished from thermal motions in the water. The energy of the waves adds to the internal energy of the water.

If the sound of an airplane does not come from the part of the sky where the plane is seen, discuss whether or not this implies that the airplane is traveling faster than the speed of sound.

The fact that you hear an airplane in a direction that differs from where you see it simply means that the airplane is moving, and not necessarily faster than sound (a sonic boom would be evidence of supersonic flight). If the speed of sound and the speed of light were the same, then you'd hear a plane where it appears in the sky. But because the two speeds are so different, the plane you see appears ahead of the plane you hear.

How does the V shape of a bow wave depend on the speed of the source?

The faster the source, the narrower the V shape.

Violinists sometimes bow a string to produce maximum vibration (antinodes) at one-quarter and three-quarters of the string length rather than at the middle of the string. Then the string vibrates with a wavelength equal to the string length rather than twice the string length. (See Figure 19.13a and b.) What is the effect on the frequency when this occurs?

The frequency is doubled

List some important differences between sound waves and light waves.

The frequency of a "classical" wave----such as a sound wave, water wave, or radio wave----matches the frequency of its vibrating source. (In the quantum world of atoms and photons, the rules are different.)

A heavy person and a light person swing to and fro on swings of the same length. Discuss who has the longer period.

The frequency of a pendulum depends on the restoring force, which is gravity. Similarly, mass doesn't affect free-fall acceleration, as is evident in Figure 19.1

What is the frequency of the second hand of a clock? The minute hand? The hour hand?

The frequency of the second hand of a clock is one cycle per minute; the frequency of the minute hand is one cycle per hour; for the hour hand the frequency is one cycle per 12 hours *To express these values in hertz, we need to convert the times to seconds. Then we find for the second hand the frequency = 1/60 hertz, for the minute hand the frequency = 1/3600 hertz, and for the hour hand the frequency = 1/(12 x 3600) = 1/(43,200) hertz*

If a water wave oscillates up and down three times each second and the distance between wave crests is 2 m, what is its frequency? What is its wavelength? What is its wave speed?

The frequency of the wave is 3 Hz, its wavelength is 2 m, and its wave speed = frequency x wavelength = 3/s x 2 m = 6 m/s

How does the frequency of vibration of a small object floating in water compare with the number of waves passing it each second?

The frequency of vibration and the number of waves passing by each second are the same.

Sonic boom

The loud sound that results from the incidence of a shock wave

Interference pattern

The pattern formed by the superposition of different sets of waves that produces reinforcement in some places and cancellation in others.

What happens to the period of a wave when the frequency decreases?

The period increases because period and frequency are reciprocals of each other.

What is meant by the period of a pendulum?

The period is the time for a complete to-and-fro swing.

The needle of a sewing machine moves up and down in simple harmonic motion. Its driving force comes from a rotating wheel that is powered by an electric motor. How do you suppose the period of the up-and-down needle compares with the period of the rotating wheel? Defend your answer.

The periods are equal. Interestingly, an edge-on view of a body moving in uniform circular motion is seen to vibrate in a straight line. How? Exactly in simple harmonic motion. So the up-and-down motion of pistons in a car engine are simple harmonic and have the same period as the circularly rotating shaft that they drive.

Wave interference

The phenomenon that occurs when two waves meet while traveling along the same medium.

In the Doppler effect, does frequency change? Does wave speed change?

The pitch (frequency) of sound is higher when a source is moving toward you, and lower when the source is moving away. *Both the frequency and the wavelength undergo a change when the source is moving, but the wave speed does not. Be clear about the distinction between frequency and speed.

Doppler effect

The shift in received frequency due to the motion of a vibrating source toward or away from a receiver.

What is the source of all waves?

The source of all waves----mechanical or electromagnetic----is something that is vibrating.

Why is lightning seen before thunder is heard?

The speed of light is 300,000 km/s, about a million times faster than sound. Because of this difference in speeds, lightning is seen a million times sooner than it is heard.

Wave speed

The speed with which waves pass a particular point: Wave speed = frequently x wavelength

Period

The time in which a vibration is completed. The period of a wave equals the period of the source and is equal to 1/frequency.

If you shake the end of a spring to produce a wave, how does the frequency of the wave compare with the frequency of your shaking hand? Does your answer depend on whether you're producing a transverse wave or a longitudinal wave? Defend your answer.

The wave frequency and the shaking frequency are the same. This sameness doesn't depend on the type of wave because the frequency of all waves is the same as the frequency of the vibrating source.

Sine curve (How does a sine curve describe a wave?)

The waveform traced by simple harmonic motion, which can be made visible on a moving conveyor belt by a pendulum swinging at right angles above the moving belt. *A sine curve is a pictorial representation of a wave*

If the speed of a wave doubles while the frequency remains the same, what happens to the wavelength?

The wavelength is lengthened to double. Speed and frequency are directly proportional.

The wavelength of a transverse wave is the distance between successive crests (or troughs). What is the wavelength of a longitudinal wave?

The wavelength of a longitudinal wave is the distance between successive compressions or rarefactions.

If you dip your finger repeatedly into a puddle of water, it creates waves. What happens to the wavelength if you dip your finger more frequently?

The wavelengths of the waves shorten

How many vibrations per second are represented in a radio wave of 101.7 MHz?

There are 101.7 million vibrations per second.

The wave patterns seen in Figures 19.4 and 19.8 are composed of circles. What does this tell you about the speed of waves moving in different directions?

They're equal

Imagine a superfast fish that is able to swim faster than the speed of sound in water. Would such a fish produce a "sonic boom"?

Yes. A supersonic fish in water would produce a shock wave and hence a sonic boom for the same reason it would if it were traveling faster than sound in air.

Astronomers find that light emitted by a particular element at one edge of the Sun has a slightly higher frequency than light from that element at the opposite edge. What do these measurements tell us about the Sun's motion?

This means that point A is moving toward earth and point B (opposite edge) is moving away from earth.

How fast must a bug swim to keep up with the waves it produces? How fast must it move to produce a bow wave?

To keep up with produced waves, the bug must swim at wave speed; to produce a bow wave, the bug must swim faster than wave speed.

Does the medium in which a wave travels move with the wave?

When a wave travels; what is transported from one location to another is a disturbance in a medium, not the medium itself.

What is the superposition principle?

When more than one wave occupies the same space at the same time the displacements add at every point.

Is it possible for one wave to cancel another wave so that no amplitude remains at certain points?

Yes. This is called destructive interference. In a standing wave in a rope, for example, parts of the rope have no amplitude----the nodes.

In terms of wavelength, show how far a wave travels in one period.

a period=one wavelength

What kind of wave is each of the following? a. The sound of one whale calling another whale under water. b. A pulse sent down a stretched rope by snapping one end of it. c. The vibrations in a guitar string

a) longitudinal b) standing wave c) transverse

Gusts of wind make the Willis Tower in Chicago sway back and forth, completing a cycle in 10 s. What are (a) its frequency and (b) its period?

a. 1/10 Hz b. 10 s.

An electric toothbrush completes 90 cycles every second. What are (a) its frequency and (b) its period?

a. 90 cycles per second is 90 Hz b. 1/90 s.

A railroad locomotive is at rest with its whistle shrieking, then starts moving toward you. a. Does the frequency of sound that you hear increase, decrease, or stay the same? b. How about the wavelength reaching your ear? c. How about the speed of sound in the air between you and the locomotive?

a. The frequency increases. b. The wavelength decreases. c. The speed is unchanged (because the air remains motionless relative to you).

What kind of motion should you impart to a stretched coiled spring (or Slinky) to provide a a. transverse wave? b. longitudinal wave?

a. To produce a transverse wave with a Slinky, shake it to and fro in a direction that is perpendicular to the length of the Slinky itself. b. To produce a longitudinal wave, shake it to and fro along the direction of its length, so that a series of compressions and rarefactions is produced.