Solved: Are beats the result of interference or of the

Problem 50E A human cannot hear sound at a frequency of 100 kHz or sound at 102 kHz. But if you walk into a room in which two sources are emitting sound waves, one at 100 kHz and the other at 102 kHz, you’ll hear sound. Explain.

Why do you not hear the sound of distant fireworks until after you see them?

Problem 1P What is the wavelength of a 340-Hz tone in air? What is the wavelength of a 34,000-Hz ultrasonic wave in air?

Problem 1R Rank the speed of sound through the following from greatest to least: a. Air b. Steel c. Water

Problem 2E If the Moon blew up, why would we not hear it?

Problem 1RQ How does a physicist usually define sound?

Problem 4E If you toss a stone in still water, concentric circles are formed. What form will waves have if a stone is tossed into smoothly flowing water?

Problem 5E Why do flying bees buzz?

Problem 4RQ Distinguish between? nfrasonic? and ?ultrasonic? sound waves.

Problem 5P You watch distant Sally Homemaker driving nails into a front porch at a regular rate of 1 stroke per second. You hear the sound of the blows exactly synchronized with the blows you see. And then you hear one more blow after you see the hammering stop. Explain how you calculate that Sally is 340 m away from you.

Problem 5RQ Distinguish between a ?compression? and a ?rarefaction.

Problem 6E A cat can hear sound frequencies up to 70,000 Hz. Bats send and receive ultra-high-frequency squeaks up to 120,000 Hz. Which hears sound of shorter wavelengths, cats or bats?

Problem 6RQ Cite evidence to support the fact that compressions and rarefactions travel in the same direction in a wave.

Problem 7E What does it mean to say that a radio station is “at 101.1 on your FM dial”?

Problem 7P What beat frequencies are possible with tuning forks of frequencies 256, 259, and 261 Hz?

Problem 4P A bat flying in a cave emits a sound and receives its echo 0.1 s later. Show that its distance from the cave wall is 19 m.

Problem 7RQ Relative to solids and liquids, how does air rank as a conductor of sound?

Problem 8E Suppose a sound wave and an electromagnetic wave have the same frequency. Which has the longer wavelength?

A grunting porpoise emits sound at 57 Hz. What is the wavelength of this sound in water, where the speed of sound is 1500 m/s?

Problem 8RQ Why will sound not travel in a vacuum?

Problem 6P Imagine a Rip van Winkle type who lives in the mountains. Just before going to sleep, he yells, “WAKE UP,” and the sound echoes off the nearest mountain and returns 8 hours later. Show that the distance between Rip and the imaginary mountain is nearly 5000 km (about the distance from New York to San Francisco).

Problem 9RQ What factors does the speed of sound depend upon? What are some factors that it does ?not? depend upon?

Problem 10E What happens to the wavelength of sound as the frequency increases?

Problem 10RQ What is the speed of sound in dry air at 0°C?

Problem 11E In the stands of a racetrack, you notice smoke from the starters gun before you hear it fire. Explain.

Problem 11RQ Does sound travel faster in warm air than in cold air? Defend your answer.

Problem 12E In Olympic competition, a microphone detects the sound of the starters gun and sends it electrically to speakers at every runners starting block. Why?

Problem 9E Sound from source A has twice the frequency of sound from source B. Compare the wavelengths of sound from the two sources.

Problem 15RQ Does sound tend to bend upward or downward when its speed is less near the ground?

Problem 16E If a bell is ringing inside a bell jar, we can no longer hear it when the air is evacuated, but we can still see it. What differences in the properties of sound and light does this indicate?

Problem 16RQ Why does sound sometimes refract under water?

Problem 17E Why is the Moon described as a “silent planet”?

Which is normally greater, the energy in ordinary sound or the energy in ordinary light?

Problem 18E As you pour water into a glass, you repeatedly tap the glass with a spoon. As the tapped glass is being filled, does the pitch of the sound increase or decrease? (What should you do to answer this question?)

Problem 18RQ What ultimately becomes of the energy of sound in the air?

Problem 19E If the speed of sound were dependent on its frequency, would you enjoy a concert sitting in the second balcony? Explain.

If the frequency of sound is doubled, what change will occur in its speed? In its wavelength?

Why does a struck tuning fork sound louder when it is held against a table?

Problem 20RQ Give at least two factors that determine the natural frequency of an object.

Problem 21E Why does sound travel slower in cold air?

Problem 21RQ How do forced ?vibrations? relate to ?resonance??

Problem 22E Why does sound travel faster in moist air? (?Hint:? At the same temperature, water vapor molecules have the same average kinetic energy as the heavier nitrogen and oxygen molecules in the air. How, then, do the average speeds of H2O molecules compare with those of N2 and O2 molecules?)

Problem 22RQ When you listen to a radio, why do you hear only one station at a time rather than hearing all stations at once?

Would the refraction of sound be possible if the speed of sound were unaffected by wind, temperature, and other conditions? Defend your answer.

Problem 23RQ How did wind-generated resonance affect the Tacoma Narrows Bridge in the stare of Washington in 1940?

Problem 24E Why can the tremor of the ground from a distant explosion be felt before the sound of the explosion can be heard?

Problem 24RQ When is it possible for one wave to cancel another?

Problem 25E What kinds of wind conditions would make sound more easily heard at long distances? Less easily heard at long distances?

Problem 25RQ What kind of waves can exhibit interference?

Problem 26E Ultrasonic waves have many applications in technology and medicine. One advantage is that large intensities can be used without danger to the ear. Cite another advantage of their short wavelength. (?Hint:? Why do microscopists use blue light rather than white light to see detail?)

What physical phenomenon underlies the production of beats?

Problem 27E If the distance from a bugle is tripled, by what factor does the sound intensity decrease? Assume that no reflections affect the sound.

Problem 27RQ What beat frequency will occur when a 370-Hz and a 374-Hz sound source are sounded together?

Problem 28E Why is an echo weaker than the original sound?

Problem 28RQ How does a radio wave differ from a sound wave?

Problem 29E What two physics mistakes occur in a science fiction movie that shows a distant explosion in outer space, where you see and hear the explosion at the same time?

Problem 30E A rule of thumb for estimating the distance in kilometers between an observer and a lightning stroke is to divide the number of seconds in the interval between the flash and the sound by 3. Is this rule correct? Defend your answer.

If a single disturbance at an unknown distance emits both transverse and longitudinal waves that travel with distinctly different speeds in the medium, such as in the ground during an earthquake, how can the distance to the disturbance be determined?

Problem 32E Why will marchers at the end of a long parade following a band be out of step with marchers near the front?

Problem 33E Why is it a sensible procedure for soldiers to break step when marching over a bridge?

Problem 34E Why is the sound of a harp soft in comparison with the sound of a piano?

Problem 35E Your classmate says that the speed of sound and the frequency of sound depend on the medium in which it travels. What part of this statement do you disagree with?

Problem 36E Apartment dwellers will testify that bass notes are more distinctly heard from music played in nearby apartments. Why do you suppose lower-frequency sounds travel through walls, floors, and ceilings more easily?

Problem 37E The sitar, an Indian musical instrument, has a set of strings that vibrate and produce music, even though they are never plucked by the player. These “sympathetic strings” are identical to the plucked strings and are mounted below them. What is your explanation?

Problem 38E Why does a dance floor heave only when certain kinds of dance steps are being performed?

Problem 40E A special device can transmit out-of-phase sound from a noisy jackhammer to its operator using earphones. Over the noise of the jackhammer, the operator can easily hear your voice while you are unable to hear his. Explain.

Problem 41E When two out-of-phase speakers are brought together as shown in Figure 20.19, which waves are most canceled, long waves or short waves? Why?

Problem 39E A pair of loudspeakers on two sides of a stage are emitting identical pure tones (tones of a fixed frequency and fixed wavelength in air). When you stand in the center aisle, equally distant from the two speakers, you hear the sound loud and clear. Why does the intensity of the sound diminish considerably when you step to one side? (? uggestion:? Use a diagram to make your point.)

Problem 42E An object resonates when the frequency of a vibrating force cither matches its natural frequency or is a submultiple of its natural frequency. Why will it not resonate to multiples of its natural frequency? (?Hint:? Think of pushing a child in a swing.)

Problem 43E How can a certain note sung by a singer cause a crystal glass to shatter?

Problem 44E Are beats the result of interference or of the Doppler effect, or of both?

Problem 45E Can it correctly be said that beats of sound are much the same thing as the rhythmic “beat” of music? Defend your answer.

Problem 46E Two sound waves of the same frequency can interfere, but, in order to produce beats, the two sound waves must be of different frequencies. Why?

Problem 47E Walking beside you, your friend takes 50 strides per minute while you take 48 strides per minute. If you start in step, you’ll soon be out of step. When will you be in step again?

Problem 48E Suppose a piano tuner hears 3 beats per second when listening to the combined sound from a tuning fork and the piano wire being tuned. After slightly tightening the string, 5 beats per second are heard. Should the string be loosened or tightened?

Problem 49E A piano tuner using a 264-Hz tuning fork hears 4 beats per second. What are two possible frequencies of vibration of the piano wire?

Problem 2P For years, marine scientists were mystified by sound waves detected by underwater microphones in the Pacific Ocean. These so-called T-waves were among the purest sounds in nature. Eventually they traced the source to underwater volcanoes, whose rising columns of bubbles resonated like organ pipes. What is the wavelength of a typical T-wave whose frequency is 7 Hz? (The speed of sound in seawater is 1530 m/s.)

What is the relationship between frequency and pitch?

Problem 2R Rank the beat frequency from highest to lowest for the following pairs of sounds: a. 132 Hz, 136 Hz b. 264 Hz, 258 Hz c. 528 Hz, 531 Hz d. 1056 Hz, 1058 Hz

Problem 3E Why would it be futile to attempt to detect sounds from other planets, even given the very best in audio detectors?

Problem 3P An oceanic depth-sounding vessel surveys the ocean bottom with ultrasonic waves that travel 1530 m/s in seawater. The time delay of the echo to the ocean floor and back is 6 s. Show that the depth of the water directly below the vessel is 4590 m.

What is the average range of a young person’s hearing?

Problem 12RQ What is an ?echo??

Problem 13E When a sound wave moves past a point in air, are there changes in the density of air at this point? Explain.

Problem 13RQ What is a ?reverberation??

Problem 14E At the instant that a high-pressure region is created just outside the prongs of a vibrating tuning fork, what is being created inside between the prongs?

Problem 14RQ What is the cause of refraction?

Problem 15E Why is it so quiet after a snowfall?

How does sound relate to energy?

What is the relationship between frequency and pitch?

What is the average range of a young person’s hearing?

Distinguish between infrasonic and ultrasonic sound waves.

Relative to solids and liquids, how does air rank as a conductor of sound?

Why doesn’t sound travel in a vacuum?

Distinguish between a compression and a rarefaction.

What factors does the speed of sound depend upon? What are some factors that it does not depend upon?

Do compressions and rarefactions travel in the same direction, or in opposite directions, in a wave?

What is the speed of sound in dry air at \(20^{\circ}\)?

Does sound travel faster in warm air than in cold air?

Which is normally greater: the energy in ordinary sound or the energy in ordinary light?

What ultimately becomes of the energy of sound in the air?

What is an echo?

What is a reverberation?

What is the cause of refraction?

Does sound tend to bend upward or downward when its speed is less near the ground?

Why does sound sometimes refract under water?

What is ultrasound?

Why does a struck tuning fork sound louder when it is held against a table?

Give at least two factors that determine the natural frequency of an object.

How do forced vibrations relate to resonance?

When you listen to a radio, why do you hear only one station at a time rather than hearing all stations at once?

How did wind-generated resonance affect the Tacoma Narrows Bridge in Washington in 1940?

When is it possible for one wave to cancel another?

What kind of waves can exhibit interference?

What physical phenomenon underlies the production of beats?

What is the result of a mirror image of a sound signal combining with the sound itself?

What beat frequency will occur when a 370-Hz and a 374-Hz sound source are sounded together?

How does a radio wave differ from a sound wave?

What is the wavelength of a 340-Hz tone in room temperature air? What is the wavelength of a 34,000-Hz ultrasonic wave in the same air?

For years, marine scientists were mystified by sound waves detected by underwater microphones in the Pacific Ocean. These so-called T-waves were among the purest sounds in nature. Eventually the scientists traced the source to underwater volcanoes, whose rising columns of bubbles resonated like organ pipes. What is the wavelength of a typical T-wave whose frequency is 7 Hz? (The speed of sound in seawater is 1530 m/s.)

An oceanic depth-sounding vessel surveys the ocean bottom with ultrasonic waves that travel at 1530 m/s in seawater. The time delay of the echo to the ocean floor and back is 6 s. Show that the depth of the water directly below the vessel is 4590 m.

A bat flying in a cave emits a sound and receives its echo 0.1 s later. Show that its distance from the cave wall is 17 m.

You watch distant Sally Homemaker driving nails into a front porch at a regular rate of 1 stroke per second. You hear the sound of the blows exactly synchronized with the blows you see. And then you hear one more blow after you see the hammering stop. Explain how you calculate that Sally is 340 m away from you.

Imagine a Rip van Winkle type who lives in a valley. Just before going to sleep, he yells, “WAKE UP,” and the sound echoes off the nearest mountain and returns 8 hours later. Show that the distance between Rip and the imaginary mountain is nearly 5000 km (about the distance from New York to San Francisco).

What beat frequencies are possible with tuning forks of frequencies 256, 259, and 261 Hz?

A grunting porpoise emits sound at 57 Hz. What is the wavelength of this sound in water, where the speed of sound is 1500 m/s?

Rank the speeds of sound through these materials, from greatest to least: a. Air b. Steel c. Water

Rank the beat frequencies from highest to lowest for the following pairs of sounds: a. 132 Hz, 136 Hz b. 264 Hz, 258 Hz c. 528 Hz, 531 Hz d. 1056 Hz, 1058 Hz

Why don’t you hear the sound of distant fireworks until after you see them?

If the Moon blew up, why wouldn’t we hear it?

Why would it be futile to attempt to detect sounds from other planets, even with the very best audio detectors?

If you toss a stone in still water, concentric circles are formed. What form will waves have if a stone is tossed into smoothly flowing water?

Why do flying bees buzz?

A cat can hear sound frequencies up to 70,000 Hz. Bats send and receive ultra-high-frequency squeaks up to 120,000 Hz. Which hears sound of shorter wavelengths: cats or bats?

What does it mean to say that a radio station is “at 101.1 on your FM dial"?

Suppose a sound wave and an electromagnetic wave have the same frequency. Which has the longer wavelength?

Sound from source A has twice the frequency of sound from source B. Compare the wavelengths of sound from the two sources.

In the stands of a racetrack, you notice smoke from the starter’s gun before you hear the gun fire. Explain.

What happens to the wavelength of sound as the frequency increases?

In Olympic competition, a microphone detects the sound of the starter’s gun and sends it electrically to speakers at every runner’s starting block. Why?

When a sound wave moves past a point in air, are there changes in the density of air at this point? Explain.

At the instant that a high-pressure region is created just outside the prongs of a vibrating tuning fork, what is being created inside between the prongs?

Why is it so quiet after a snowfall?

If a bell is ringing inside a bell jar, we can no longer hear it when the air is evacuated, but we can still see it. What differences in the properties of sound and light does this indicate?

Why is the Moon described as a “silent planet”?

If the speed of sound were dependent on its frequency, would you enjoy a concert sitting in the second balcony? Explain.

If the frequency of sound is doubled, what change will occur in its speed? In its wavelength?

Why does sound travel slower in cold air than in warm air?

Would the refraction of sound be possible if the speed of sound were unaffected by wind, temperature, and other conditions? Defend your answer.

What kinds of wind conditions would make sound more easily heard at long distances? Less easily heard at long distances?

Why can the tremor of the ground from a distant explosion be felt before the sound of the explosion can be heard?

If the distance from a bugle is tripled, by what factor does the sound intensity decrease? Assume that no reflections affect the sound.

Why is an echo weaker than the original sound?

If a single disturbance at an unknown distance emits both transverse and longitudinal waves that travel with distinctly different speeds in the medium, such as in the ground during an earthquake, how can the distance to the disturbance be determined?

What two physics mistakes occur in a science fiction movie that shows a distant explosion in outer space and you see and hear the explosion at the same time?

Why will marchers at the end of a long parade following a band be out of step with marchers near the front?

Why is it a sensible procedure for soldiers to break step when marching over a bridge?

Why is the sound of a harp soft in comparison with the sound of a piano?

Your classmate says that the speed of sound and the frequency of sound depend on the medium in which the sound travels. What part of this statement do you disagree with?

The sitar, an Indian musical instrument, has a set of strings that vibrate and produce music, even though they are never plucked by the player. These “sympathetic strings” are identical to the plucked strings and are mounted below them. What is your explanation?

Apartment dwellers will testify that bass notes are more distinctly heard from music played in nearby apartments. Why do you suppose lower-frequency sounds travel through walls, floors, and ceilings more easily than high frequency sounds?

Why does a dance floor heave only when certain kinds of dance steps are being performed?

A special device can transmit out-of-phase sound from a noisy jackhammer to its operator using earphones. Over the noise of the jackhammer, the operator can easily hear your voice while you are unable to hear his. Explain.

An object resonates when the frequency of a vibrating force either matches its natural frequency or is a submultiple of its natural frequency. Why won’t it resonate to multiples of its natural frequency? (Hint: Think of pushing a child in a swing.)

How can a certain note sung by a singer cause a crystal glass to shatter?

Are beats the result of interference, of the Doppler effect, or of both?

Is it correct to say that beats of sound are much the same thing as the rhythmic “beat” of music? Defend your answer.

Two sound waves of the same frequency can interfere, but, in order to produce beats, the two sound waves must have different frequencies. Why?

Suppose a piano tuner hears 3 beats per second when listening to the combined sound from a tuning fork and the piano wire being tuned. After slightly tightening the string, 5 beats per second are heard. Should the string be loosened or tightened?

A piano tuner using a 264-Hz tuning fork hears 4 beats per second. What are two possible frequencies of vibration of the piano wire?

As you pour water into a glass, you repeatedly tap the glass with a spoon. As the tapped glass is being filled, does the pitch of the sound increase or decrease? (Discuss what you should do to answer this question.)

A human cannot hear sound at a frequency of 100 kHz or sound at 102 kHz. But if you walk into a room in which two sources are emitting sound waves, one at 100 kHz and the other at 102 kHz, you’ll hear sound. Explain.

Discuss why sound travels faster in moist air. (Note that at the same temperature, water vapor molecules have the same average kinetic energy as the heavier nitrogen and oxygen molecules in the air.) How, then, do the average speeds of \(H_2O\) molecules compare with the speeds of \(N_2\) and \(O_2\) molecules?

Ultrasonic waves have many applications in technology and medicine. One advantage is that large intensities can be used without danger to the ear. Cite another advantage of their short wavelength. (Hint: Why do microscopists use blue light rather than white light to see detail?)

A rule of thumb for estimating the distance in kilometers between an observer and a lightning stroke is to divide the number of seconds in the interval between the flash and the sound by 3. Is this rule correct? Discuss the reason for its correctness or incorrectness.

A pair of loudspeakers on two sides of a stage are emitting identical pure tones (tones of a fixed frequency and fixed wavelength in air). When you stand in the center aisle, equally distant from the two speakers, you hear the sound loud and clear. Why does the intensity of the sound diminish considerably when you step to one side? (Suggestion: Use a diagram to make your point.)

When two out-of-phase speakers are brought together as shown in Figure 20.19, which waves are most canceled: long waves or short waves? Defend and discuss your answer.