Exam 1 Review

Physics 2020 Summer 2011
Richard Ingebretsen
REVIEW FOR MIDTERM 1
1. A 2.00 m long tube is open at both ends. The frequency of a certain harmonic is 410.0 Hz, and the
frequency of the next higher harmonic is 492.0 Hz. Determine the speed of sound in the air column.
2. At rest, a car's horn sounds the note A (440.0 Hz). The horn is sounded while the car is moving down the
street. A bicyclist moving in the same direction with 1/3 the car's speed hears a frequency of 414.0 Hz.
(Speed of sound = 343 m/s)
A. How fast is the car moving?
B. Is the cyclist ahead or behind the car?
3. A. Two loud speakers are placed above and below one another as shown. They are driven
by the same source at a frequency of 500.0 Hz. (V sound = 343 m/s)
1. What minimum distance should the top speaker be moved toward A in order to
create destructive interference between the two speakers?
2. If the top speaker is moved back twice the distance calculated in part (1) above,
will constructive or destructive interference occur?
B. On a work day, the average decibel level of a busy street is 70.0 dB with 100 cars
passing by a given point every minute. If the number of cars is reduced to 25 every
minute on a weekend, what is the new decibel level?
4. A stretched string fixed both ends has a mass of 40.0 g and length of 8.0 m. The tension in the string is
49.0 N.
A. Determine the positions of all the nodes and antinodes for the third harmonic as measured from
one of the fixed ends.
B. What is the vibration frequency for this harmonic?
5. An ambulance is traveling toward a truck. Both the ambulance and truck are traveling at the same speed.
The truck sounds its horn (f = 508.0 Hz). The ambulance driver hears the truck’s horn as 542.0 Hz. The
speed of sound in air is 343.0 m/s. How fast is each going?
6. A weird phenomena occurs when wind blows across a power line. A standing wave is set up much like on
a guitar string which produces a rumbling sound. Assume that a power line (: = .002 kg/m) has a tension
of 323.0 N, and the poles are 19.0 m apart. The lowest frequency that a human ear can hear is 20.0 Hz.
What is the lowest harmonic number n that could be responsible for this low rumbling sound?
7. (a) The external auditory canal (in addition to being a storage place for earwax) serves to increase the
ear’s sensitivity to sound. The canal is about 2.5 cm long and regarded as a tube open at one end
and closed at the eardrum. Around what frequency is the human ear sensitized to by this method
(speed of sound: 343.0 m/s).
(b) What is the length required for an organ pipe to produce a sound of this frequency [from (a)]? The
pipe is open at both ends (the speed of sound is 343.0 m/s).
8. A. The human ear can detect differences in sound intensities as small a 1.0 dB. What is the ratio of
the sound intensities.
B. The human ear can hear “beats” when two sounds are playing on slightly different frequencies. If
two sounds have wavelengths of 0.776 and 0.769 n, what beat frequency is heard? The speed of
sound is 343 m/s.

9. An ambulance siren emits a note of 500 Hz when at rest. Take v sound = 343 m/s.
A. When the ambulance is moving at 10.0 m/s, what frequency is heard by an observer traveling at
15.0 m/s toward the source?
B. When the ambulance is moving at 10.0 m/s, what frequency is heard by an observer traveling at
15.0 m/s after the observer has passed the ambulance and recedes from it?
10. A. Two identical mandolin strings under 200 N of tension are sounding tones with fundamental
frequencies of 523 Hz. The peg of one string slips slightly and the tension in it drops to 196 N.
How many beats are heard each second?
B. You are sitting on the coast of Mombasa, Kenya listening to the sounds of pregnant Anopheles
mosquitos ready to infect you with malaria. You know that a typical sound level for this mosquito
is 40 dB, and normal conversation as approximately 50 dB. How many buzzing Anopheles
mosquitoes will produce a sound intensity equal to that of normal conservation?
11. A 0.30 g wire is stretched between two points 70.0 cm apart. If the tension in the wire is 600 N, find the
wires first, second and third harmonics.
12. A. Two eagles fly directly toward one another, the first at 15.0 m/s and the second at 20.0 m/s. Both
birds screech, one emitting a frequency of 3200 Hz and the other at 3800 Hz. What frequency do
they receive if the speed of sound is 330 m/s?
B. If a large horsefly 3.0 m away from you makes a noise of 40.0 dB, what is the noise level of 1000
flies at that distance?
13. A crude approximation of voice production is to consider the breathing passages and mouth to be a
resonating tube closed at one end.
(a)
What is the fundamental frequency if the tube is 0.240 m long.
Boltzmann's constant = 1.38 × 10 -23 J/K
Mass of helium (M He ) = 3.32 × 10 -27
air temperature = 37.0°C kg; ( = 1.4
14. A. Twenty violins playing simultaneously with the same intensity combine to give an intensity level
of 82.5 dB.
(a) What is the intensity level of each violin?
(b) If the number of violins is increased to 40, will the combined intensity level be more than,
less than or equal to 165 dB? Explain.
B. To tune middle C on a piano, a tuner hits the key and at the same time sounds a 261 Hz tuning
fork. If the tuner hears 3 beats per second, what are the possible frequencies of the piano key?
15. Two cars traveling with the same speed move directly away from one another. One car sounds a horn
whose frequency is 205 Hz and a person in the other car hears a frequency of 192 Hz. What is the speed of
the cars?
16. A 12.5 g clothesline is stretched with a tension of 22.1 N between two poles 7.66 m apart.
(a)
(b)
(c)
(d)
(e)
What is the frequency of the fundamental?
What is the frequency of the second harmonic?
If the tension in the clothesline is increased, do the frequencies in parts (a) and (b) increase,
decrease, or stay the same?
Will the frequencies increase, decrease, or stay the same if a more massive rope is used?
The mass of the clothesline is changed to 15.0 g. Repeat (a) through (d) above using this new
mass.

17. An open organ pipe (open at both ends) has a harmonic with a frequency of 440 Hz. The next higher
harmonic in the pipe has a frequency of 528 Hz.
(a)
(b)
Find the frequency of the fundamental.
What is the length of the pipe?
18. An organ pipe (A), which is open at both ends, is playing its 2 nd harmonic. The wavelength of the 2 nd
harmonic is 0.1000 m Another organ pipe (B), which is closed at one end, is playing its 3 rd harmonic. The
wavelength of the 3 rd harmonic is 0.09968 m. The speed of sound is 343 m/s in both pipes.
(a)
(b)
(c)
Draw the standing wave pattern in each of the tubes and identify at least one node and antinode in
each drawing.
What is the length of each pipe?
What is the beat frequency heard when both pipes play at the same time?
19. An ambulance is traveling with its siren on. Initially you are standing still and observe a frequency of 0.9
times the frequency as compared to what the driver of the ambulance hears. v sound = 343 m/s.
(a)
(b)
(c)
Is the ambulance moving towards you or away from you?
What is the speed of the ambulance?
You later begin to run in the opposite direction as the ambulance at a speed of 3.0 m/s. What
frequency do you hear now if the siren has a frequency of 900 Hz?
20. At a concert you are standing 4.0 m away from a speaker and hear the music at 120 dB. (Note: The
threshold of human hearing is at an intensity of 10 -12 W/m 2 .)
(a)
(b)
(c)
Assuming the sound of the speaker moves outward in all directions, what is the power of the
speaker?
How far away from the speaker should you stand to listen to the music at a more safe 80 dB?
If there were 3 identical speakers with the same power output as found in part (a) and you stand
4.0 m away, how many decibels do you hear the music playing at?
21. A guitar string has a tension of 80 N and has a mass of 6.0 g and is 0.4 m
long.
(a)
(b)
(c)
What is the speed of a wave on this string?
What is the fundamental frequency of this string?
Two identical guitars, as described above, play a note in phase
at their fundamental frequencies. If the guitars and a listener
are positioned as shown in the drawing, what is the largest
possible distance (d), such that the listener hears no sound?
(Note: The speed of sound in air = 343 m/s.)
22. Farid plays a banjo at the top of a round well that is open to the air. He
plucks a string at its fundamental frequency (mass = 5.0 grams; length = 0.40 m; tension = 125 N) and
notices that the sound seems louder than usual. This phenomena happens again when he plucks another
string at its fundamental frequency (mass = 4.0 grams; length = 0.40 m; tension = 196 N). It happens yet
again when he plays a note at that produces a frequency of 225 Hz. Speed of sound = 343 m/s
(a)
(b)
(c)
(d)
What is the wavelength of the 2nd harmonic on the 5.0 gram string?
How deep is the well?
Find the fundamental frequency of the well.
Calculate the wavelength of the fundamental frequency of the well.

23. A rocket in a fireworks display explodes high in the air. The sound spreads out uniformly in all directions.
Eric is standing 150 m away from the explosion and observes the intensity of the sound to be 2.0 W/m 2 .
Elliot is standing at a different location that is 100 m away from the explosion. The threshold of human
hearing is 1 × 10 -12 W/m 2 .
(a)
(b)
(c)
(d)
What intensity level does Eric hear?
What is the power of sound produced by the explosion?
What the intensity level does Elliot hear?
An intensity level of 180 dB causes irreversible damage to the ears including hearing loss. How
close to the explosion would Elliot have to be to suffer this type of injury?
24. Two trains are traveling in opposite directions on parallel tracks. Train A is heading east and sounds its
horn at a frequency of 1000 Hz. Train B is traveling west at 30 m/s and is also sounding its horn. Speed of
sound in air = 343 m/s
(a)
(b)
(c)
(d)
Josh is standing by the tracks as both trains are heading towards him. He observes a frequency of
1050 Hz coming from train A, how fast is it moving?
Josh observes a frequency of 1200 Hz coming from train B as it is approaching him. What
frequency does the conductor of train B hear coming from his own train?
As the two trains are approaching one another, what frequency does the conductor of train A hear
coming from train B?
After the two trains have passed each other and are now moving away from each other, what
frequency does the conductor of train B hear coming from train A?
25. Standing waves are set up on three strings fixed at each end at their fundamental
frequencies, as shown in the drawing. The tensions in the strings are the same
and all strings have the same linear density. However, their lengths vary.
For parts a-c, circle the correct answer:
(a)
(b)
(c)
The waves on the string B have a (larger speed, same speed, smaller
speed, not enough information to tell) compared to those on string A.
String B vibrates at (a higher frequency, the same frequency, a lower
frequency, not enough information to tell) compared to string A.
The beat frequency produced by the two standing waves on strings C
and A will be (greater than, the same as, less than, not enough
information to tell) the beat frequency produced by strings B and A.
As stated above, all strings have the same linear density and tension. String A has a fundamental frequency
of 210 Hz. The speed of the waves on string A is 42 m/s. String B is 0.60 cm longer than string A. String
C is 1.20 cm longer than string A.
(d) What is the frequency of a wave on string C?
(e) What is the beat frequency between strings B and A?
26. A If an ocean wave hits a particular beach once every four seconds and the wave peaks are 12 m
apart, what is the velocity of the waves coming into shore?
(a) 3 m/s (b) 4 ms/ (c) 12 m/s (d) 48 m/s
B. Sound waves are an example of
(a)
(b)
(c)
(d)
longitudinal waves because the medium moves perpendicularly to the propagation of the
wave.
longitudinal waves because the medium moves parallel to the propagation of the wave.
transverse waves because the medium moves perpendicularly to the propagation of the
wave.
transverse waves because the medium moves parallel to the propagation of the wave.

C. If a guitar string is 0.5 m long, what is the wavelength of its third harmonic?
(a) 0.25 m (b) 0.33 m (c) 0.5 m (d) 1 m
D. Two violinists are playing together and are slightly out of tune. If one violinist produces a
frequency of 883 Hz and the other produces a frequency of 879 Hz, the frequency of the beats
heard would be
(a) 2 Hz (b) 4 Hz (c) 81 Hz (d) 1762 Hz
E. Two waves are traveling toward each other on the same string. Wave A has an amplitude of 3 cm
and a wavelength of 10 cm, and wave B has an amplitude and wavelengths twice that of wave A.
What is the maximum displacement of the string when the waves interfere with each other?
(a) 0 cm (b) 3 cm (c) 6 cm (d) 9 cm
F. A vibrating string has consecutive harmonics at wavelengths of 2.0 m and 4.0 m. What is the
length of the string?
(a) 1.0 m (b) 2.0 m (c) 4.0 m (d) 8.0 m
27. A guitar string has a tension of 100 N and has a mass of 7.0 g and is 0.45 m long. speed of sound in air =
343 m/s
(a)
(b)
(c)
What is the speed of a wave on this string?
What is the frequency of the third harmonic on this string?
Two identical guitars, as described above, play a note in phase
at their fundamental frequencies. If the guitars and a listener are
positioned as shown in the drawing, what is the largest possible
distance (d), such that the listener hears no sound?
28. A rocket in a fireworks display explodes high in the air. The sound
spreads out uniformly in all directions. Aaron is standing 150 m away from the explosion and observes the
intensity of the sound to be 2.0 W/m 2 . Justin is standing at a different location and observes the intensity
level to be 90 dB. threshold of human hearing is 1 × 10 -12 W/m 2
(a)
(b)
(c)
(d)
What intensity level does Aaron hear?
What is the power of sound produced by the explosion?
How far away from the explosion is Justin?
An intensity level of 180 dB causes irreversible damage to the ears including hearing loss. How
close to the explosion would Justin have to be to suffer this type of injury?
29. Two trains are traveling in opposite directions on parallel tracks . Train A is heading east and sounds its
horn at a frequency of 1000 Hz. Train B is traveling west at 30 m/s and is also sounding its horn.
speed of sound in air = 343 m/s
(a) When both trains are headed towards each other the conductor of train A observes a frequency of
1200 Hz coming from train B. Farid is standing by the tracks as both trains are heading towards
him. Both trains sound their horns and Farid observes a beat frequency of 15 Hz. How fast is
train A moving?
(b) What beat frequency does Farid hear when both trains are traveling away from him?
speed of sound in air = 343 m/s

30. A The speed of a transverse wave on a string is 470 m/s, and the wavelength is 0.13 m. The
amplitude of the wave is 1 mm. How much time is required for a particle of the string to move
through a total distance of 1.0 km? This distance is accomplished by the particle moving up and
down only.
B. A wire is stretched between two posts. Another wire is stretched between two posts that are four
times as far apart. The tension in the wires is the same, and they have the same mass. A
transverse wave travels on the shorter wire with a speed of 200 m/s. What would be the speed of
the wave on the longer wire?
C. The drawing shows two graphs that
represent a transverse wave on a string.
The wave is moving in the +x direction.
(a)
(b)
What is the amplitude of the
wave?
What is the speed of the wave?
D. An amplified guitar has a sound intensity level that is 16 dB greater than the same unamplified
sound. If the unamplified sound has an intensity of 10 -6 W/m 2 , what is the amplified intensity?
31. A. Inside a busy restaurant, a small mouse is dancing around. Assume the noise it makes has a power
of 0.042 W and radiates uniformly outward in all directions. How much power goes into
one ear (area = 2.1 × 10 -3 m 2 ) of a person sitting 10 m away from the mouse?
B. A tube is open only at one end. A certain harmonic produced by the tube has a frequency of 495
Hz. The next higher harmonic has a frequency of 825 Hz. The speed of sound in air is 343 m/s.
(a)
(b)
What is the integer n that describes the harmonic whose frequency is 495 Hz?
Find is the length of the tube.
C. In the figure, suppose that the separation between speakers A and B is 7.00 m and the
speakers are vibrating in phase. They are playing identical 135 Hz tones, and the speed of
sound is 343 m/s. The observer starts from 300 m away from speaker B at a point C and
walks in a straight line toward speaker B. How far away is he from speaker B when he
comes to the second spot where he hears no
sound?
32. A. At a concert you are standing 4.0 m away from a speaker and hear the music at 120 dB. (Note:
The threshold of human hearing is at an intensity of 10 -12 W/m 2 .)
(a)
(b)
(c)
Assuming the sound of the speaker moves outward in all directions, what is the power of
the speaker?
How far away from the speaker should you stand to listen to the music at a more safe
80 dB?
f there were 3 identical speakers with power output of 100 W each and you stand 4.0 m
away, how many decibels do you hear the music playing at?
B. A row of seats is parallel to a stage at a distance of 9.0 m from it. At the center and front of the
stage is a diffraction horn loudspeaker. This speaker sends out its sound through an opening that is
like a small doorway with a width D of 0.073 m. The speaker is playing a tone that has a frequency
of 3.00 × 10 4 Hz. The speed of sound is 343 m/s. What is the separation between two seats,
located near the center of the row, at which the tone cannot be heard?

33. A. The fundamental frequency of a string fixed at both ends is 388 Hz. How long does it take for a
wave to travel the length of this string?
B. A string has a linear density of 8.80 × 10 -3 kg/m and is under a
tension of 265 N. The string is 2.1 m long, is fixed at both ends,
and is vibrating in the standing wave pattern shown in the
drawing.
(a)
(b)
(c)
Determine the speed of the traveling wave.
Find the wavelength of the traveling wave.
Calculate the frequency of the traveling wave
C. You are flying in an ultra-light aircraft at a speed of 44 m/s. An eagle, whose speed is 13 m/s, is
flying directly toward you. Each of the given speeds is relative to the ground. The eagle emits a
shrill cry whose frequency is 3400 Hz. The speed of sound is 330 m/s. [going toward each other
v j 6 7v eg ]
(a)
(b)
What frequency do you hear?
Part of the cry is reflected from the jet and returns to the eagle. What frequency does the
eagle hear for this reflected wave?
34. A The speed of a transverse wave on a string is 470 m/s, and the wavelength is 0.13 m. The
amplitude of the wave is 1 mm. How much time is required for a particle of the string to move
through a total distance of 1.0 km? This distance is accomplished by the particle moving up and
down only.
B. A wire is stretched between two posts. Another wire is stretched between two posts that are four
times as far apart. The tension in the wires is the same, and they have the same mass. A
transverse wave travels on the shorter wire with a speed of 200 m/s. What would be the speed of
the wave on the longer wire?
C. The drawing shows two graphs that
represent a transverse wave on a string.
The wave is moving in the +x direction.
(a) What is the amplitude of the
wave?
(b) What is the speed of the wave?
D. An amplified guitar has a sound intensity
level that is 16 dB greater than the same unamplified sound. If the unamplified sound has an
intensity of 10 -6 W/m 2 , what is the amplified intensity?
35. A. Inside a busy restaurant, a small mouse is dancing around. Assume the noise it makes has a power
of 0.042 W and radiates uniformly outward in all directions. How much power goes into one ear
(area = 2.1 × 10 -3 m 2 ) of a person sitting 10 m away from the mouse?
B. A tube is open only at one end. A certain harmonic produced by the tube has a frequency of 495
Hz. The next higher harmonic has a frequency of 825 Hz. The speed of sound in air is 343 m/s.
(a) What is the integer n that describes the harmonic whose frequency is 495 Hz?
(b) Find is the length of the tube.
C. [9 pts.] In the figure, suppose that the separation between speakers A
and B is 7.00 m and the speakers are vibrating in phase. They are
playing identical 135 Hz tones, and the speed of sound is 343 m/s. The
observer starts from 300 m away from speaker B at a point C and walks
in a straight line toward speaker B. How far away is he from speaker B
when he comes to the second spot where he hears no sound?

36. A. At a concert you are standing 4.0 m away from a speaker and hear the music at 120 dB. (Note:
The threshold of human hearing is at an intensity of 10 -12 W/m 2 .)
(a) Assuming the sound of the speaker moves outward in all directions, what is the power of
the speaker?
(b) How far away from the speaker should you stand to listen to the music at a more safe 80
dB?
(c) If there were 3 identical speakers with power output of 100 W each and you stand 4.0 m
away, how many decibels do you hear the music playing at?
B. A row of seats is parallel to a stage at a distance of 9.0 m from it. At the center and front of the
stage is a diffraction horn loudspeaker. This speaker sends out its sound through an opening that is
like a small doorway with a width D of 0.073 m. The speaker is playing a tone that has a frequency
of 3.00 × 10 4 Hz. The speed of sound is 343 m/s. What is the separation between two seats,
located near the center of the row, at which the tone cannot be heard?
37. A. The fundamental frequency of a string fixed at both ends is 388 Hz. How long does it take for a
wave to travel the length of this string?
B. A string has a linear density of 8.80 × 10 -3 kg/m and is under a
tension of 265 N. The string is 2.1 m long, is fixed at both ends, and
is vibrating in the standing wave pattern shown in the drawing.
(a) Determine the speed of the traveling wave.
(b) Find the wavelength of the traveling wave.
(c) Calculate the frequency of the traveling wave
C. You are flying in an ultra-light aircraft at a speed of 44 m/s. An eagle, whose speed is 13 m/s, is
flying directly toward you. Each of the given speeds is relative to the ground. The eagle emits a
shrill cry whose frequency is 3400 Hz. The speed of sound is 330 m/s. [going toward each other
v j 6 7v eg ]
(a)
(b)
What frequency do you hear?
Part of the cry is reflected from the jet and returns to the eagle. What frequency does the
eagle hear for this reflected wave?
38. A. The mass of a string is 5.6 × 10 -3 kg, and it is stretched so the tension in it is 185 N. A transverse
wave traveling on this string has a frequency of 260 Hz and a wavelength of 0.60 m. What is the
length of the string?
B. Two speakers, one directly behind the other, are in phase and each generating a 245 Hz sound
wave. What is the smallest separation distance between the speakers that will produce destructive
interference at a listener standing in front of them? Assume that the speed of sound is 341 m/s.
C. A 34 cm length of wire has a mass of 6.0 g. It is stretched between two fixed supports and is under
a tension of 185 N. What is the fundamental frequency of this wire?
D. A recording engineer works in a soundproofed room that is 52.0 dB quieter than the outside. If the
sound intensity in the room is 1.40 × 10 -10 W/m 2 , what is the intensity outside?
39. A. Suppose that sound is emitted uniformly in all directions by a public address system. The intensity
at a location 24 m away from the sound source is 2.8 × 10 -4 W/m 2 . If a person is standing 85 m
away, how much energy goes through one ear (area = 0.1 cm 2 ) in 2 hours?
B. Two loudspeakers on a concert stage are vibrating in phase. A listener is 54.5 m from the left
speaker and 27 m from the right speaker. The listener can respond to all frequencies from 20 to
20,000 Hz, and the speed of sound is 343 m/s. What is the third lowest frequency that cannot be
heard at this location, but that can be heard if he moves somewhere else between the speakers?
C. The fundamental frequency of a string fixed at both ends is 388 Hz. How long does it take for a
wave to travel the length of this string?z

40. A. Rich plays a banjo at the top of a round well that is open to the air. He plucks a string at its
fundamental frequency (mass = 5.0 grams; length = 0.40 m; tension = 125 N) and notices that the
sound seems louder than usual. This phenomena happens again when he plucks another string at
its fundamental frequency (mass = 4.0 grams; length = 0.40 m; tension = 196 N). It happens yet
again when he plays a note at a frequency of 225 Hz. Speed of sound = 343 m/s.
1. How deep is the well?
2. Find the fundamental frequency of the well.
B. A speaker on a car produces a frequency of 21 Hz. The speed of sound is 343 m/s. When Bill is
driving toward a brick wall, he hears a beat frequency of 3 Hz caused by the original sound and the
reflected sound from the brick wall. How fast is Bill driving?
41. A. A 3.00 kHz tone is being produced by a speaker with a radius of 0.080 m. The air temperature
changes from 0 to 29°C. Assuming air to be an ideal gas (m = 4.78 × 10 -26 kg, ( = 1.4), find the
change in the diffraction angle 2. for the first minima.
B. Two loudspeakers are vibrating in phase. They are set up as in the figure, and point C
is located as shown there. Assume the speed of sound is 343 m/s. The speakers play
the same tone. What is the second smallest frequency that will produce destructive
interference at point C?
42. A. A person lying on an air mattress in the ocean rises and falls through one complete cycle every 5
seconds. The crests of the wave causing the motion are 20.0 m apart. Determine the speed of the
wave.
B. Suppose that sound is emitted uniformly in all directions by a public address system. The
intensity at a location 20 m away from the sound source is 2.7 × 10 -4 W/m 2 . What is the
intensity at a spot that is 73 m away?
C. A wire is stretched between two posts. Another wire is stretched between two posts that are four
times as far apart. The tension in the longer wire is twice the tension in the shorter wire,
and the wires have the same mass. A transverse wave travels on the shorter wire with a
speed of 210 m/s. What would be the speed of the wave on the longer wire?
D. When a person wears a hearing aid, the sound intensity level increases by 21.0 dB. By what
factor does the sound intensity increase?
43. A. A 2.50 m long tube is open at one end. The frequency of a certain harmonic is 429 Hz, and the
frequency of the next higher harmonic is 495 Hz. Determine the speed of sound in the air column.
B. A hunter is standing on flat ground between two vertical cliffs that are directly opposite one another.
He is closer to one cliff than to the other. He fires a gun and, after a while, hears three echoes. The
second echo arrives 2 s after the first, and the third echo arrives 0.9 s after the second. Assuming
that the speed of sound is 343 m/s and that there are no reflections of sound from the ground, find
the distance between the cliffs.
C. A strange phenomenon occurs when wind blows across a power line. A standing wave is set up
much like on a guitar string which produces a rumbling sound. Assume that a power line with linear
mass density .002 kg/m has a tension of 323.0 N, and the poles are 25.0 m apart. The lowest
frequency that a human ear can hear is 20.0 Hz. What is the minimum number of antinodes that this
wave could have if it is responsible for this low rumbling sound

44. A. In the figure, suppose that the separation between speakers A
and B is 4.60 m and the speakers are vibrating in phase. They
are playing identical 172 Hz tones, and the speed of sound is
344 m/s. What is the closest possible distance between speaker
B and the observer at C, such that he observes destructive
interference?
B. Two cars move directly away from one another. One car sounds a horn whose frequency is 205 Hz
and a person in the other car hears a frequency of 192 Hz. The speed of sound is 343 m/s. The car
which sounds its horn is moving twice as fast as the other car. What is the speed of the slower car?
45. A. Inside a busy restaurant, a small mouse is dancing around. Assume the noise it makes has a power
of 0.042 W and radiates uniformly outward in all directions. How much energy goes into one ear
(area = 2.1 × 10 -3 m 2 ) of a person sitting 10 m away from the mouse in a period of 30 minutes?
B. Speakers A and B are vibrating in phase. They are directly facing each other, are 0.90 m apart, and
are each playing a 686 Hz tone. The speed of sound is 343 m/s. On the line between the speakers
there are locations where constructive interference occurs. What are the distances of these locations
from speaker A?

46. A. Measurements show that the speed of sound in a certain material is 323m/s. A sound frequency of
1500 Hz is applied to the material. Find the wavelength of the sound in the material.
B. An uncomfortably loud sound might have an intensity of 0.54 W/m 2 . If a sound from the speakers is
emitted in all directions at a rock concert and is 1.20 W/m 2 at 5 m from the speakers, how far would a
person have to stand for the sound to be merely uncomfortably loud?
C. Two little boys have stretched a string between their adjacent windows 5 m apart and attached cans to
transmit their voices. The boys do not like that they can hear each other through the window before they
can hear each other through the cans. If the speed of sound in the string is 170 m/s and the speed of sound
in air is 340m/s, by how much do they need to increase the tension in the string (T new /T old ) in order to
match the speed of sound through their windows?
D, When a person wears a hearing aid, the sound intensity level is increased by 19.0 dB. By what factor
does the sound intensity increase?
47. A. A long tube in air is open at both ends. A harmonic frequency is measured at 330 Hz, and the next higher
harmonic is measured at 396 Hz.
1. If the speed of sound in air is 340 m/s in the tube, how long is the tube?
2. What is the fundamental frequency?
B. A sonic device for measuring room size is often employed by appraisers. The device emits short high
pitched sound pulses which bounce off a far wall and are detected by the device. Assume the speed of
sound in air is 340 m/s, and the device detects the echo at 0.06 seconds after emission. How far is the
opposite wall?
C. A strange phenomenon occurs when wind blows across a power line. A standing wave is set up much
like on a guitar string which produces a rumbling sound. Assume that a power line with linear mass
density of 2.50 × 10 -3 kg/m has a tension of 345 N and distance between the poles is 20.0 m. The lowest
frequency the human ear can hear is 20.0Hz. Find the minimum number of antinodes in the wire that
could have produced this low rumbling sound.
48. A. Two sound sources (speakers) in this figure emit sound at the same
frequency and are in phase with each other. Sound source A starts at
position B and is slowly being moved to the left. The listener is 2.50 m
from speaker B. The listener hears the first constructive interference node
at d 1 = 40.0 cm. What is d 1 when the listener hears the second destructive
interference node?
B. A tuning fork of frequency 400 Hz is moved away from a stationary
observer towards a flat wall at a speed of 2.00 m/s. Assume the speed of
sound in air is 340 m/s. What is the beat frequency between the tuning
fork and the reflected sound as heard by the stationary observer?
49. A. A mother is in a car with her child who speaks non-stop for 45 minutes. The mother’s ear is 75 cm from
the child’s mouth. The noise the child makes has a power of 0.50 W and radiates outward in all
directions. How much energy goes into one ear (area = 2.0 × 10 -3 m 2 ) of the mother during the 45
minutes?
B. Two sound sources (speakers) directly face each other and are a distance of 10 m apart. The speakers are
playing identical tones that have 170 Hz. Speed of sound in air is 340 m/s. Along the line between the
two speakers are locations where destructive interference occurs. What are the locations of the
destructive interference from the speaker on the right?

50. A. Tsunamis are fast-moving waves generated by underwater earthquakes. In the deep ocean their amplitude
is barely noticeable, but upon reaching shore, they can rise up to the astonishing height of a six-story
building. One tsunami wave, generated off the Aleutian Islands in Alaska, had a wavelength of
9.0 × 10 2 km and traveled a distance of 3700 km in 5.2 h. Find the period of the wave.
B. Speaker 1 is placed directly behind speaker 2. Each speaker generates a 215 Hz sound wave. A listener
is standing directly in front of the speakers. What is the smallest separation distance between the speakers
that will produce destructive interference? Assume that the speed of sound is 338 m/s.
C. The fundamental frequency of a string fixed at both ends is 373 Hz. How long does it take for a wave to
travel the length of this string?
D. A person hums into the top of a well and finds that standing waves are established at frequencies of 48,
80, and 112 Hz (with no frequencies between these). The frequency of 48 Hz is not necessarily the
fundamental frequency. The speed of sound is 343 m/s. How deep is the well?
51. A. Two cars are both moving in the same direction. Car A is moving twice as fast as car B. The speed of
sound is 343 m/s. Car A sounds a horn (frequency 205 Hz) and a person in the car B hears a frequency of
192 Hz.
1. Car B is ahead of car A. True False (circle one)
2. What is the speed of car A?
B. In the figure, suppose that the separation between speaker B and the
observer is 7.00 m and the speakers are vibrating in phase. They are
playing identical 135 Hz tones, and the speed of sound is 343 m/s.
Speaker A is positioned somewhere to the left of speaker B as shown.
What is the closest distance speaker A can be to speaker B so that the
observer hears no sound?
52. A. Two identical mandolin strings under 200 N of tension are sounding tones with fundamental frequencies
of 523 Hz. The peg of one string slips slightly and the tension in it drops to 196 N. How many beats are
heard each second?
B. You are sitting on the coast of Mombasa, Kenya listening to the sounds of pregnant Anopheles
mosquitoes ready to infect you with malaria. You know that a typical sound level for this mosquito is
40 dB when the mosquito is 2.0 meters away, and normal conversation is approximately 50 dB. How
many buzzing Anopheles mosquitoes will produce a sound intensity equal to that of normal conservation
if the mosquitoes are 8.0 meters away?
C. Speakers A and B are vibrating in phase. They are directly facing each other, are 0.90 m apart, and are
each playing a 686 Hz tone. The speed of sound is 343 m/s. On the line between the speakers there are
locations where constructive interference occurs. What are the distances of these locations from speaker
A?

53. A. During the recent U2 concert, a student could hear the music from his couch at approximately
conversation level (50 dB). The student estimated that he was about a mile away from the concert
(1600 m). Assume the sound from the concert moves outward in all directions and that none of the sound
was blocked by any buildings.
1. What dB level would a concert attendee hear if they were 16 m from source of the sound?
2. If the student heard 50 dB on his couch during the entire 3 hour concert, how much energy was
produced in 3 hours?
B. Johy plays a banjo at the top of a round well that is open to the air. She plucks a string at its fundamental
frequency (mass = 8.0 grams; length = 0.40 m; tension = 200 N) and notices that the sound seems louder
than usual. This phenomena happens again when she plucks another string at its fundamental frequency
(mass = 4.0 grams; length = 0.40 m; tension = 196 N). It happens yet again when she plays a note at that
produces a frequency of 225 Hz. Speed of sound = 343 m/s.
1. What is the wavelength of the 2nd harmonic on the 8.0 gram string?
2. How deep is the well?
54. A. Tsunamis are fast-moving waves generated by underwater earthquakes. In the deep ocean their
amplitude is barely noticeable, but upon reaching shore, they can rise up to the astonishing height of a sixstory
building. One tsunami, generated off the Aleutian Islands in Alaska, had a wavelength of 9.0 × 10 2
km and traveled a distance of 3700 km in 5.2 h. Find the wave's period.
B. Suppose that a public address system emits sound uniformly in all directions and that there are no
reflections. The intensity at a location 24 m away from the sound source is 3.1 × 10 -4 W/m 2 . What is the
intensity at a spot that is 82 m away?
C. Two loudspeakers face each other, vibrate in phase, and produce identical 440 Hz tones. A listener walks
from one speaker toward the other at a constant speed and hears the loudness change (loud-soft-loud) at a
frequency of 2.2 Hz. The speed of sound is 343 m/s. What is the walking speed?
D. To measure the acceleration due to gravity on a distant planet, an astronaut hangs a 0.065 kg ball from the
end of a wire. The wire has a length of 1.5 m and a linear density of 3.10 × 10 -4 kg/m. Using electronic
equipment, the astronaut measures the time for a transverse pulse to travel the length of the wire and
obtains a value of 0.070 s. The mass of the wire is negligible compared to the mass of the ball.
Determine the acceleration due to gravity.
55. A. The sound produced by a mosquito results from its wing beats. The frequency of the wing beat of a
female mosquito (400 Hz) is different from that of a male (600 Hz). This frequency difference is used by
mosquitoes for gender identification. A female and a male mosquito are flying directly toward each other
at the same speed. The male mosquito misidentifies the female for a male. The speed of sound is 334
m/s. How fast are the mosquitoes traveling?
B. In the figure below two in-phase loudspeakers, A and B, are separated
by 10.50 m. Keyton is stationed at point C, which is 2.32 m in front of
speaker B. The triangle ABC is a right triangle. Both speakers are
playing identical 206-Hz tones, and the speed of sound is 343 m/s.
Speaker A is slowly moved further to the left, while ABC remains a
right triangle. What is the separation between the speakers when
destructive interference occurs at point C for the first time since
moving speaker A?

56. A. Two identical mandolin strings under 250 N of tension are sounding tones with fundamental frequencies
of 500 Hz. The peg of one string slips slightly and the tension in it drops to 245 N. How many beats are
heard each second?
B. A recording engineer works in a soundproofed room that is 49.5 dB quieter than the outside. If the sound
intensity in the room is 1.50 × 10 -10 W/m 2 , what is the intensity outside?
C. Speakers A and B are vibrating in phase. They are directly facing each other, are 8.2 m apart, and are
each playing a 77.0 Hz tone. The speed of sound is 343 m/s. On the line between the speakers there are
three points where constructive interference occurs. What are the distances of these three points from
speaker A?
57. A. A student watching a baseball game hears the ball hit the bat at 70 dB. As expected, the student is sitting
in the nose bleed seats and is about 160 m from the batter. Assume the sound from the collision moves
outward in all directions and that none of the sound was blocked by any buildings.
1. What dB level would the pitcher hear if he were 18 m from source of the sound?
2. How much sound energy was produced during the collision if the sound lasted for 0.02 seconds?
B. Shawn plays a banjo at the top of a round well that is open to the air. He plucks a string at its
fundamental frequency (mass = 5.0 grams; length = 0.40 m; tension = 125 N) and notices that the sound
seems louder than usual. This phenomena happens again when he plucks another string at its fundamental
frequency (mass = 4.0 grams; length = 0.40 m; tension = 196 N). It happens yet again when he plays a
note at that produces a frequency of 225 Hz. Speed of sound = 343 m/s
1. How deep is the well?
2. Find the fundamental frequency of the well.