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Exam 16: Superposition and Standing Waves

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Question 1

Multiple Choice

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A string fixed at both ends is vibrating in one of its harmonics. If we now increase only the frequency at which the string is vibrating, which of the following characteristics do we also increase? (There could be more than one correct choice.)

A) the speed of the traveling waves on the string
B) the period of the traveling waves on the string
C) the wavelength of the traveling waves on the string
D) the amplitude of the traveling waves on the string
E) none of the above

F) B) and E)
G) A) and E)

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E

Question 2

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An organ pipe closed at one end and open at the other end has two successive harmonics with frequencies of 2170 Hz and 2790 Hz. What is the fundamental frequency of the pipe?

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310 Hz

Question 3

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Standing waves of frequency 17 Hz are produced on a string that has a mass per unit length of $0.0160 \mathrm {~kg} / \mathrm { m }$ To what tension must the string be stretched between two supports if adjacent nodes in the standing wave are to be 0.87 m apart?

If a string fixed at both ends resonates in its fundamental mode with a frequency of 150 Hz, at which of the following frequencies will it not resonate? (There could be more than one correct choice.)

An organ pipe of length L that is open at one end resonates in its third harmonic with a wavelength of 2L/3. Is the other end of the pipe closed or open?

When a guitar is tuned to adjust it pitch, what is it that is changed?

A pipe of length L that is closed at one end and open at the other end is resonating at its fundamental frequency. Which statement about the sound is correct?

Two in-phase loudspeakers that emit sound with the same frequency are placed along a wall and are separated by a distance of 5.00 m. A person is standing 12.0 m away from the wall, equidistant from the loudspeakers. When the person moves 1.00 m parallel to the wall, she experiences destructive interference for the first time. What is the frequency of the sound? The speed of sound in air is 343 m/s.

A string that is 2.0 meters long is fixed at both ends and tightened until the wave speed is $18 \mathrm {~m} / \mathrm { s }$ What is the frequency of the standing wave shown in the figure?

What is the length of the shortest pipe closed on one end and open at the other end that will have a fundamental frequency of 0.060 kHz on a day when the speed of sound is 340 m/s?

A string of linear density 1.5 g/m is under a tension of 20 N. What should be its length if its fundamental resonance frequency is 220 Hz?

One of the harmonics of a column of air in a tube that is open at one end and closed at the other has a frequency of 448 Hz, and the next higher harmonic has a frequency of 576 Hz. What is the fundamental frequency of the air column in this tube?

The lowest tone to resonate in 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?

Two stereo speakers mounted 4.52 m apart on a wall emit identical sound waves. You are standing at the opposite wall of the room at a point directly between the two speakers. You walk 2.11 m parallel to the wall, to a location where you first notice that the sound intensity is essentially zero. If the wall along which you are walking is $10.7 \mathrm {~m}$ from the wall with the speakers, what is the wavelength of the sound waves? The walls are cushioned to absorb sound reflections.

A pipe that is 0.92 m long and open at both ends vibrates in the second overtone with a frequency of $584 \mathrm {~Hz}$ What is the speed of sound in the air in this pipe?

A music tuner uses a 554-Hz C# tuning fork to tune the frequency of a musical instrument. If the tuner hears a beat frequency of 2 Hz, what is the frequency of the instrument?

If a guitar string has a fundamental frequency of 500 Hz, which one of the following frequencies can set the string into resonant vibration?

A 25-g string is stretched with a tension of 43 N between two fixed points 12 m apart. What is the frequency of the second harmonic?

Consider two pipes of the same length: one pipe is open at both ends and the other pipe is closed on one end but open at the other end. If the fundamental frequency of the totally open pipe is 300 Hz, what is the fundamental frequency of the other pipe?

Two strings both vibrate at exactly 819 Hz. The tension in one of them is then increased slightly. As a result, six beats per second are heard when both strings vibrate. What is the new frequency of the string that was tightened?