Exam 16: Superposition and Standing Waves

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 string of length 2.5 m is fixed at both ends. When the string vibrates at a frequency of 85 Hz, a standing wave with five loops is formed. (a) Determine the distance between two adjacent nodes. (b) Determine the wavelength of the waves that travel on the string. (c) Determine the speed of traveling waves on this string. (d) Determine the fundamental frequency of this string.

A 2.0-g string that is 0.67 m long is under tension. The string vibrates at 700 Hz tone in its third harmonic, and this vibration causes a sound wave. What is the wavelength of the sound? The speed of sound in air is 344 m/s.

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?

An organ pipe open at both ends has a length of 0.80 m. If the velocity of sound in air is $340 \mathrm {~m} / \mathrm { s } \text {, }$ what is the frequency of the second harmonic of this pipe?

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.) A) 75 Hz B) 300 Hz C) 450 Hz D) 500 Hz E) 600 Hz

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 in-phase loudspeakers are 3.0 m apart. They emit sound with a frequency of 490 Hz. A microphone is placed half-way between the speakers and then moved along the line joining the two speakers until the first point of constructive interference is found. At what distance from that midpoint is that first point? The speed of sound in air is 343 m/s.

Find the first three harmonics of a string of linear mass density 2.00 g/m and length 0.600 m when the tension in it is 50.0 N.

Two loudspeakers placed 6.00 m apart are driven in phase by an audio oscillator having a frequency range from 1595 Hz to 2158 Hz. A point P is located 4.70 m from one loudspeaker and 3.60 m from the other speaker. The speed of sound in the room is 344 m/s. At what frequency (or frequencies) of the oscillator does the sound reaching point P interfere destructively? (There could be more than one correct choice.)

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?

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?

Two in-phase loudspeakers that emit sound with the same frequency are placed along a wall and are separated by a distance of 8.00 m. A person is standing 12.0 m away from the wall, equidistant from the loudspeakers. When the person moves 3.00 m parallel to the wall, she experiences destructive interference for the second time. What is the frequency of the sound? The speed of sound in air is 343 m/s.

An organ pipe that is 1.75 m long and open at both ends produces sound of frequency 303 Hz when resonating in its second overtone. What is the speed of sound in the room?

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?

A 4.0-g string is 0.36 m long and is under tension. The string vibrates at 500 Hz in its third harmonic. What is the wavelength of the standing wave in the string?

The wavelengths of the sounds produced by two horns are 6.0 m and 7.0 m, respectively. What beat frequency is heard when the horns are sounded on a day when the speed of sound is 340 m/s?

Two in-phase loudspeakers are placed along a wall and are separated by a distance of 4.00 m. They emit sound with a frequency of 514 Hz. A person is standing away from the wall, in front of one of the loudspeakers. What is the closest nonzero distance from the wall the person can stand and hear constructive interference? The speed of sound in air is 343 m/s.

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.

The speed of propagation of a transverse wave on a 2.0-m long string fixed at both ends is 200 m/s. Which one of the following is not a resonant frequency of this string?