Exam 16: Superposition and Standing Waves

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?

Two tuning forks have frequencies of 440 and 522 Hz. What is the beat frequency if both are sounding simultaneously?

A 0.13-m string, fixed at both ends and vibrating in its n = 4 harmonic, excites a pipe that is $0.88 \mathrm {~m}$ long and open at both ends, into its second overtone resonance. What is the speed of transverse waves on the string? The speed of sound in air is 345 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?

A violin with string length 32 cm and string density $1.5 \mathrm {~g} / \mathrm { cm }$ resonates in its fundamental with the first overtone of a 2.0-m organ pipe with one end closed and one end open. What is the tension in the string if the speed of sound in air is 344 m/s?

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 tone to resonate in a pipe of length L that is closed at one end but open at the other end is 200 Hz. Which one of the following frequencies will not resonate in that pipe?

A person stands between two speakers driven by the same source. Each speaker produces a tone with a frequency of 200 Hz on a day when the speed of sound is 330 m/s. The person is 1.65 m from one speaker and 4.95 m from the other. What type of interference does the person perceive?

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?

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?

A 4.0-g string is 0.39 m long and is under tension. The string vibrates at 600 Hz in its third harmonic. What is the tension in this string?

One of the harmonics of a string fixed at both ends has a frequency of 52.2 Hz and the next higher harmonic has a frequency of 60.9 Hz. What is the fundamental frequency of the string?

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. How long is the tube? The speed of sound in air is 343 m/s.

If the frequency of a violin string is to be increased by 20%, what change in tension must be applied?

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.

Consider a pipe of length L that is open at one end and closed at the other end. What are the wavelengths of the three lowest-pitch tones produced by this pipe?

What is the frequency of the fundamental mode of vibration of a steel piano wire stretched to a tension of 440 N? The wire is 0.600 m long and has a mass of 5.60 g.

A string that is 0.26 m long is vibrating in its n = 6 harmonic. The sound from tthis string excites a pipe that is $0.88 \mathrm {~m}$ long and open at both ends into its second overtone resonance. What is the common resonant frequency of the string and the pipe? The speed of sound in air is 345 m/s.

A standing wave is oscillating at 950 Hz on a string, as shown in the figure. What is the wave speed?

A stretched string is observed to have four equal segments in a standing wave driven at a frequency of 480 Hz. What driving frequency will set up a standing wave with five equal segments?