Ch. 17

Question 1

Does the principle of linear superposition imply that two sound waves, passing through the same place at the same time, always create a louder sound than is created by either wave alone?

Answer 1

No, because if the two sound waves have the same amplitude and frequency, they might cancel and no sound will be heard.

Question 2

Suppose that you are sitting at the overlap point between two speakers. Because of destructive interference, you hear no sound, even though both speakers are emitting identical sound waves. One of the speakers is suddenly shut off. Will you now hear a sound?

Answer 2

Yes

Question 3

Starting at the overlap point, you walk along a straight path that is perpendicular to the line between the speakers and passes through the midpoint of that line. As you walk, the loudness of the sound..

Answer 3

Does not change

Question 4

Starting at the overlap point, you walk along a path that is parallel to the line between the speakers. As you walk, the loudness of the sound..

Answer 4

Changes from loud to faint to loud

Question 5

At an open air rock concert you are standing directly in front of a speaker. You hear the high frequency sounds of a female vocalist as well as the low frequency sounds of the rhythmic bass. As you walk to one side of the speaker, the sounds of the vocalist ___, and those of the rhythmic bass ___.

Answer 5

Drop off noticeably; drop off only slightly

Question 6

Which type of radio, AM or FM, diffracts more readily around a given obstacle?

Answer 6

AM, because it has a greater wavelength

Question 7

A tuning fork has a frequency of 440Hz. The string of a violin and this tuning fork, when sounded together, produce a frequency of 1Hz. From these two pieces of information alone, is it possible to determine the exact frequency of the violin string?

Answer 7

No, because the frequency of the violin string could be either 439 or 441Hz

Question 8

When the regions of constructive and destructive interference move past a listeners ear, a beat frequency of 2Hz is heard. Suppose that the tuning forks are sounded underwater and that the listener is also underwater. The forks vibrate at 438 and 440Hz, just as they do in air. However, sound travels four times faster in water than in air. The beat frequency heard by the underwater listen is ___.

Answer 8

2Hz

Question 9

A standing wave that corresponds to the 4th harmonic is set up on a string that is fixed at both ends.

How many loops are in this standing wave?

Answer 9

4

Question 10

A standing wave that corresponds to the 4th harmonic is set up on a string that is fixed at both ends.

How many nodes (excluding the nodes at the ends of the string) does this standing wave have?

Answer 10

3

Question 11

A standing wave that corresponds to the 4th harmonic is set up on a string that is fixed at both ends.

Is there a node or an antinode at the midpoint of the string?

Answer 11

Node

Question 12

A standing wave that corresponds to the 4th harmonic is set up on a string that is fixed at both ends.

If the frequency of this standing wave is 440Hz, what is the frequency of the lowest-frequency standing wave that could be set up on this string?

Answer 12

110Hz

Question 13

The tension in a guitar string is doubled. By what factor does the frequency of the vibrating string change?

Answer 13

It increases by a factor of sqrt(2)

Question 14

A string is vibrating back and forth. The tension in the string is decreased by a factor of 4, with the frequency and length of the spring remaining the same. A new standing wave pattern develops on the string. How many loops are in this new pattern?

Answer 14

2

Question 15

A rope is hanging vertically straight down. The top end is being vibrated back and forth, and a standing wave with many loops develops on the rope, analogous to a standing wave in a horizontal rope. The rope has mass. The separation between successive nodes is..

Answer 15

Greater near the top of the rope than near the bottom

Question 16

A cylindrical bottle, partially filled with water, is open at the top. When you blow across the top of the bottle a standing wave is set up inside it.

Is there a node or an antinode at the top of the bottle?

Answer 16

Antinode

Question 17

A cylindrical bottle, partially filled with water, is open at the top. When you blow across the top of the bottle a standing wave is set up inside it.

Is there a node or an antinode at the surface of the water?

Answer 17

Node

Question 18

A cylindrical bottle, partially filled with water, is open at the top. When you blow across the top of the bottle a standing wave is set up inside it.

If the standing wave is vibrating at its fundamental frequency, what is the distance between the top of the bottle and the surface of the water? Express your answer in terms of the wavelength of the standing wave.

Answer 18

(1/4)wavelength

Question 19

A cylindrical bottle, partially filled with water, is open at the top. When you blow across the top of the bottle a standing wave is set up inside it.

If you take a sip from the bottle, is the fundamental frequency of the standing wave raised, lowered, or does it remain the same?

Answer 19

Lowered

Question 20

Both tubes are filled with air, in which the speed of sound is vair.
Frequency fork next to vair has “frequency = f”. Suppose, instead, the tube near the tuning fork labeled “Frequency = 2f” is filled not with air, but with another gas in which the speed of sound is vgas. The frequency of each tuning fork remains unchanged. How should vgas compare with vair in order that the standing wave pattern in each tube has the same appearance?

Answer 20

vgas = 2vair

Question 21

Standing waves can ruin the acoustics of a concert hall if there is an excessive reflection of the sound waves that the performers generate. For example, suppose that a performer generates a 2093Hz tone. If a large-amplitude standing wave is present, it is possible for a listener to move a distance of only 4.1cm and hear the loudness of the time change from loud to faint. What does the distance or 4.1cm represent?

Answer 21

One-fourth the wavelength of the sound

Question 22

A wind instrument is brought into a warm house from the cold outdoors. What happens to the natural frequencies of the instrument? Neglect any change in the length of the instrument.

Answer 22

They increase

Question 23

Two cellists, one seated directly behind the other in an orchestra, play the same note for the conductor, who is directly in front of them. Because of the separation between the cellists, destructive interference occurs at the conductor. This separation is the smallest that produces destructive interference. Would this separation increase, decrease, or remain the same if the cellists produced a note with a higher frequency?

Answer 23

The separation would decrease because the wavelength of the sound is smaller.

As the frequency does up, the wavelength goes down, so the separation between the cellists decreases.

Question 24

A loudspeaker is producing sound of a certain wavelength. Which combination of the wavelength lambda (expressed as a multiple of lambda0) and the speakers diameter D (expressed as a multiple of D0) would exhibit the greatest amount of diffraction when the sound leaves the speaker and enters the room?

Answer 24

Lambda = 2lambda0
D = D0

Question 25

Sound of a given frequency leaves a loudspeaker and spreads out due to diffraction. The speaker is placed in a room that contains either air or helium. The speed of sound in helium is about three times as great as the speed of sound in air. In which room, if either, does the sound exhibit the greater diffraction when leaving the speaker?

Answer 25

The greater diffraction occurs in the helium-filled room, because the wavelength of the sound is greater in that room.

Question 26

Two musicians are comparing their trombones. The first produces a tone that is known to be 438Hz. When the two trombones play together they produce 6 beats every 2 seconds. Which statement is true about the second trombone?

Answer 26

It is producing either a 435Hz sound or a 441Hz sound.

The trombones produce 6 beats every 2 seconds, so the beat frequency is 3Hz.

438Hz-3Hz = 435Hz
438Hz+3Hz = 441Hz

Question 27

Two transverse standing waves.
The strings have the same tension and length, but the bottom string is more massive. Which standing wave, if either, is vibrating at the higher frequency?

Answer 27

The top standing wave has the higher frequency, because the traveling waves have a larger speed due to the smaller mass of the string.

Question 28

A standing wave on a string fixed at both ends is vibrating at its fourth harmonic. If the length, tension, and linear density are kept constant, what can be said about the wavelength and frequency of the fifth harmonic relative to the fourth harmonic?

Answer 28

The wavelength of the fifth harmonic is shorter, and its frequency is higher.