Question 1

A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thinner and lighter. What is the orientation of the reflected and transmitted pulses?
A) Both pulses are right side up.
B) The reflected pulse returns right side up while the transmitted pulse is inverted.
C) The reflected pulse returns inverted while the transmitted pulse is right side up.
D) Both pulses are inverted.

Accepted Answer

A

Question 2

Consider a pipe of length L that is open at both ends. What are the wavelengths of the three lowest-pitch tones produced by this pipe?
A) 4L, 2L, L
B) 2L, L, L/2
C) 2L, L, 2L/3
D) 4L, 4L/3, 4L/5
E) 4L, 2L, L/2

Accepted Answer

For a pipe open at both ends, the wavelengths of the tones produced correspond to the standing waves that fit exactly within the length of the pipe. The fundamental frequency (lowest pitch) corresponds to a wavelength of 2L, where the pipe length is half a wavelength. The next harmonics are integer multiples of the fundamental frequency, so the second harmonic has a wavelength of L (2/2 * L), and the third harmonic has a wavelength of 2L/3 (3/2 * L).

Question 3

The lowest-pitch tone to resonate in a pipe of length L that is closed at one end and open at the other end is 200 Hz. Which one of the following frequencies will NOT resonate in the same pipe?
A) 400 Hz
B) 600 Hz
C) 1000 Hz
D) 1400 Hz
E) 1800 Hz

Accepted Answer

A

Question 4

A platinum wire that is 1.20 m long has a radius of 0.500 mm and is fixed at both ends. In its third harmonic it vibrates at 512 Hz. The density of platinum is 21.4 × 10³ kg/m³. What is the tension in the wire? A) 4.00 kN B) 2.00 kN C) 2.82 kN D) 1.41 kN E) 1.00 kN

Accepted Answer

The frequency of the third harmonic is given by: $f_n$ = n(v/2L), where n is the harmonic number, v is the wave velocity, and L is the length of the wire. Solving for v, we get v = 2Lf_n/n = 2(1.20 m)(512 Hz)/3 = 410 m/s.

The tension in the wire is given by T = (pi*r^2*d)*v^2/L, where r is the radius, d is the density, and L is the length of the wire. Substituting the given values, we get T = (pi*(0.500*10^-3 m)^2*(21.4*10^3 kg/m^3))*(410 m/s)^2/1.20 m = 2.82 kN.

Therefore, the answer is C, 2.82 kN.

Question 5

A guitar string is fixed at both ends. If you tighten it to increase its tension
A) the frequencies of its vibrational modes will increase but its wavelengths will not be affected.
B) the wavelength increases but the frequency is not affected.
C) both the frequency and the wavelength increase.

Accepted Answer

The frequency of a guitar string is directly proportional to the tension and inversely proportional to the wavelength. Therefore, increasing the tension will increase the frequency of its vibrational modes but will not affect its wavelength. Choice B is incorrect because increasing tension would actually decrease the wavelength, not increase it. Choice C is also incorrect as it suggests that both frequency and wavelength increase, which is not the case.

Question 6

A 2.00-m long piano wire with a mass per unit length of 12.0 g/m is under a tension of 8.00 kN. What is the frequency of the fundamental mode of vibration of this wire?
A) 204 Hz
B) 102 Hz
C) 408 Hz
D) 510 Hz
E) 153 Hz

Accepted Answer

The answer of A 2.00-m long piano wire with a...

Question 7

Consider the waves on a vibrating guitar string and the sound waves the guitar produces in the surrounding air. The string waves and the sound waves must have the same
A) wavelength.
B) velocity.
C) frequency.
D) amplitude.
E) More than one of the above is true.

Accepted Answer

The frequency of the string waves determines the frequency of the sound waves produced by the guitar, therefore they must have the same frequency. The wavelength and velocity of the waves can be different in different mediums. The amplitude can also be different between the string waves and the sound waves.

Question 8

A pipe that is 120 cm long resonates to produce sound of wavelengths 480 cm, 160 cm, and 96 cm but does not resonate at any wavelengths longer than these. This pipe is
A) open at both ends.
B) open at one end and closed at the other end.
C) closed at both ends.
D) We cannot tell because we do not know the frequency of the sound.

Accepted Answer

The pipe resonates at wavelengths that are odd multiples of a quarter of its length (120 cm), which is characteristic of a pipe that is open at one end and closed at the other. The given wavelengths (480 cm, 160 cm, and 96 cm) correspond to 1/4, 3/4, and 5/4 times the length of the pipe, respectively, fitting the pattern for a pipe open at one end and closed at the other.

Question 9

A 1.0-g string that is 0.64 m long is fixed at both ends and is under tension. This string produces a 100-Hz tone when it vibrates in the third harmonic. The speed of sound in air is 344 m/s. The tension in the string, in is closest to
A) 2.8 N.
B) 2.3 N.
C) 1.8 N.
D) 3.4 N.
E) 3.9 N.

Accepted Answer

The speed of a wave on a string is given by $v = \sqrt{\frac{T}{\mu}}$, where $T$ is the tension in the string and $\mu$ is the linear mass density of the string. For the third harmonic on a string fixed at both ends, the frequency $f$ is given by $f = \frac{3v}{2L}$, where $L$ is the length of the string. Rearranging the formula for $v$ to solve for $T$ and substituting the given values, we find $T$ is closest to 2.8 N.

Question 10

A tube open at one end and closed at the other end produces sound having a fundamental frequency of 350 Hz. If you now open the closed end, the fundamental frequency becomes
A) 87.5 Hz.
B) 175 Hz.
C) 350 Hz.
D) 700 Hz.
E) 1400 Hz.

Accepted Answer

When a tube is closed at one end, the fundamental frequency of the sound produced is given by:

f = v/4L

where f is the fundamental frequency, v is the speed of sound, and L is the length of the tube.

Now, if you open the closed end of the tube, the effective length of the tube becomes half of its original length. So, the new fundamental frequency can be found using the same formula with L/2 instead of L:

f' = v/2(L/2) = 2v/4L = v/2f

where f' is the new fundamental frequency and f is the original fundamental frequency.

Therefore, the new fundamental frequency is:

f' = 350 Hz / 2 = 175 Hz

So, the correct answer is B.

Question 11

A 2.0-m string is fixed at both ends and tightened until the wave speed is  What is the frequency of the standing wave shown in the figure? 
A) 120 Hz
B) 230 Hz
C) 350 Hz
D) 470 Hz

Accepted Answer

The answer of A 2.0-m string is fixed at both...

Question 12

Two pure tones are sounded together and a particular beat frequency is heard. What happens to the beat frequency if the frequency of one of the tones is increased?
A) It increases.
B) It decreases.
C) It does not change.
D) It becomes zero.
E) We cannot tell from the information given.

Accepted Answer

The answer of Two pure tones are sounded together and...

Question 13

The lowest-pitch tone to resonate in a pipe of length L that is open at both ends is 200 Hz. Which one of the following frequencies will NOT resonate in the same pipe?
A) 400 Hz
B) 600 Hz
C) 800 Hz
D) 900 Hz
E) 1000 Hz

Accepted Answer

The resonant frequencies for a pipe open at both ends are given by:
f = (n/2L) * v
where n is any positive integer (1, 2, 3...), L is the length of the pipe, and v is the speed of sound in the medium (air, in this case).

For the fundamental (lowest frequency) mode, n = 1, so:
200 Hz = (1/2L) * v
Solving for L:
L = v/(2*200 Hz) = v/400 Hz

For the first overtone (second harmonic), n = 2, so:
f = (2/2L) * v = v/L = 2 * 200 Hz = 400 Hz

For the second overtone (third harmonic), n = 3, so:
f = (3/2L) * v = 3 * 200 Hz = 600 Hz

For the third overtone (fourth harmonic), n = 4, so:
f = (4/2L) * v = 2 * 400 Hz = 800 Hz

For the fourth overtone (fifth harmonic), n = 5, so:
f = (5/2L) * v = 5 * 200 Hz = 1000 Hz

Therefore, all of the given frequencies except for 900 Hz are overtone frequencies that should resonate in the same pipe. To check whether 900 Hz will resonate, we can use the formula:
f = (n/2L) * v
where n = 5 (since it's the fifth overtone) and L is still v/400. Solving for f:
f = (5/2)(v/(v/400)) = 1000 Hz
So the only frequency that should not resonate in this pipe is 900 Hz.

Question 14

A guitar string 0.650 m long has a tension of 61.0 N and a mass per unit length of 3.00 g/m.
(a) What is the speed of waves on the string when it is plucked?
(b) What is the string's fundamental frequency of vibration when plucked?

Accepted Answer

The answer of A guitar string 0.650 m long has...

Question 15

In a resonating pipe that is open at one end and closed at the other end, there
A) are displacement nodes at each end.
B) are displacement antinodes at each end.
C) is a displacement node at the open end and a displacement antinode at the closed end.
D) is a displacement node at the closed end and a displacement antinode at the open end.

Accepted Answer

In a resonating pipe that is open at one end and closed at the other end, there is a displacement node at the closed end because there is no air movement at that point, and a displacement antinode at the open end because that is where the air movement is the highest.

Question 16

A thin 2.00-m string of mass 50.0 g is fixed at both ends and under a tension of 70.0 N. If it is set into small-amplitude oscillation, what is the frequency of the first harmonic mode?
A) 6.61 Hz
B) 13.2 Hz
C) 26.5 Hz
D) 52.9 Hz

Accepted Answer

The frequency of the first harmonic mode is given by:
$$f =\frac{1}{2L}\sqrt{\frac{T}{\mu}}$$
where L is the length of the string, T is the tension, and μ is the linear density (mass per unit length).
In this case, L = 2.00 m, T = 70.0 N, and μ = m/L = 50 g / 2.00 m = 0.025 kg/m.
Substituting these values into the equation gives:
$$f =\frac{1}{2(2.00	ext{ m})}\sqrt{\frac{70.0	ext{ N}}{0.025	ext{ kg/m}}} \approx \boxed{	extbf{(B) } 13.2	ext{ Hz}}$$

Question 17

A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thicker and heavier. What is the orientation of the reflected and transmitted pulses?
A) Both pulses are right side up.
B) The reflected pulse returns right side up while the transmitted pulse is inverted.
C) The reflected pulse returns inverted while the transmitted pulse is right side up.
D) Both pulses are inverted.

Accepted Answer

When a wave pulse travels from a less dense to a more dense medium, some of the wave energy is reflected back into the less dense medium while the remaining energy is transmitted into the more dense medium. At this discontinuity, the reflected pulse will return inverted because the wave pulse experiences a phase change upon reflection. The transmitted pulse will be right side up because the speed of the wave changes when it enters a different medium, but there is no phase change.

Question 18

A standing wave is oscillating at 690 Hz on a string, as shown in the figure. What is the speed of traveling waves on this string? 
A) 280 m/s
B) 410 m/s
C) 210 m/s
D) 140 m/s

Accepted Answer

The answer of A standing wave is oscillating at 690...

Question 19

In a resonating pipe that is open at both ends, there
A) are displacement nodes at each end.
B) are displacement antinodes at each end.
C) is a displacement node at one end and a displacement antinode at the other end.
D) None of the above are possible.

Accepted Answer

In a resonating pipe that is open at both ends, there are displacement antinodes at each end because the air at the ends can move freely, creating maximum displacement at these points.

Question 20

A thin taut string is fixed at both ends and stretched along the horizontal x-axis with its left end at x = 0. It is vibrating in its third OVERTONE, and the equation for the vertical displacement of any point on the string is y(x,t) = (1.22 cm) sin[(14.4 m^-1)x] cos[(166 rad/s)t]. (a) What are the frequency and wavelength of the fundamental mode of this string? (b) How long is the string? (c) How fast do waves travel on this string?

Accepted Answer

The answer of A thin taut string is fixed at...

Quiz 17: Superposition

A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thinner and lighter. What is the orientation of the reflected and transmitted pulses?

Consider a pipe of length L that is open at both ends. What are the wavelengths of the three lowest-pitch tones produced by this pipe?

The lowest-pitch tone to resonate in a pipe of length L that is closed at one end and open at the other end is 200 Hz. Which one of the following frequencies will NOT resonate in the same pipe?

A platinum wire that is 1.20 m long has a radius of 0.500 mm and is fixed at both ends. In its third harmonic it vibrates at 512 Hz. The density of platinum is 21.4 × 103 kg/m3. What is the tension in the wire?

A guitar string is fixed at both ends. If you tighten it to increase its tension

A 2.00-m long piano wire with a mass per unit length of 12.0 g/m is under a tension of 8.00 kN. What is the frequency of the fundamental mode of vibration of this wire?

Consider the waves on a vibrating guitar string and the sound waves the guitar produces in the surrounding air. The string waves and the sound waves must have the same

A pipe that is 120 cm long resonates to produce sound of wavelengths 480 cm, 160 cm, and 96 cm but does not resonate at any wavelengths longer than these. This pipe is

A 1.0-g string that is 0.64 m long is fixed at both ends and is under tension. This string produces a 100-Hz tone when it vibrates in the third harmonic. The speed of sound in air is 344 m/s. The tension in the string, in is closest to

A tube open at one end and closed at the other end produces sound having a fundamental frequency of 350 Hz. If you now open the closed end, the fundamental frequency becomes

A 2.0-m string is fixed at both ends and tightened until the wave speed is What is the frequency of the standing wave shown in the figure?

Two pure tones are sounded together and a particular beat frequency is heard. What happens to the beat frequency if the frequency of one of the tones is increased?

The lowest-pitch tone to resonate in a pipe of length L that is open at both ends is 200 Hz. Which one of the following frequencies will NOT resonate in the same pipe?

A guitar string 0.650 m long has a tension of 61.0 N and a mass per unit length of 3.00 g/m. (a) What is the speed of waves on the string when it is plucked? (b) What is the string's fundamental frequency of vibration when plucked?

In a resonating pipe that is open at one end and closed at the other end, there

A thin 2.00-m string of mass 50.0 g is fixed at both ends and under a tension of 70.0 N. If it is set into small-amplitude oscillation, what is the frequency of the first harmonic mode?

A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thicker and heavier. What is the orientation of the reflected and transmitted pulses?

A standing wave is oscillating at 690 Hz on a string, as shown in the figure. What is the speed of traveling waves on this string?

In a resonating pipe that is open at both ends, there

A platinum wire that is 1.20 m long has a radius of 0.500 mm and is fixed at both ends. In its third harmonic it vibrates at 512 Hz. The density of platinum is 21.4 × 10³ kg/m³. What is the tension in the wire?