3.5 Sound interference and resonance: standing waves in air columns  (Page 6/11)

A piano tuner hears a beat every 2.00 s when listening to a 264.0-Hz tuning fork and a single piano string. What are the two possible frequencies of the string?

(a) What is the fundamental frequency of a 0.672-m-long tube, open at both ends, on a day when the speed of sound is 344 m/s? (b) What is the frequency of its second harmonic?

If a wind instrument, such as a tuba, has a fundamental frequency of 32.0 Hz, what are its first three overtones? It is closed at one end. (The overtones of a real tuba are more complex than this example, because it is a tapered tube.)

What are the first three overtones of a bassoon that has a fundamental frequency of 90.0 Hz? It is open at both ends. (The overtones of a real bassoon are more complex than this example, because its double reed makes it act more like a tube closed at one end.)

How long must a flute be in order to have a fundamental frequency of 262 Hz (this frequency corresponds to middle C on the evenly tempered chromatic scale) on a day when air temperature is $\mathrm{20.0ºC}$ ? It is open at both ends.

What length should an oboe have to produce a fundamental frequency of 110 Hz on a day when the speed of sound is 343 m/s? It is open at both ends.

What is the length of a tube that has a fundamental frequency of 176 Hz and a first overtone of 352 Hz if the speed of sound is 343 m/s?

(a) Find the length of an organ pipe closed at one end that produces a fundamental frequency of 256 Hz when air temperature is $\mathrm{18.0ºC}$ . (b) What is its fundamental frequency at $\mathrm{25.0ºC}$ ?

By what fraction will the frequencies produced by a wind instrument change when air temperature goes from $\mathrm{10.0ºC}$ to $\mathrm{30.0ºC}$ ? That is, find the ratio of the frequencies at those temperatures.

The ear canal resonates like a tube closed at one end. (See [link] .) If ear canals range in length from 1.80 to 2.60 cm in an average population, what is the range of fundamental resonant frequencies? Take air temperature to be $\mathrm{37.0ºC}$ , which is the same as body temperature. How does this result correlate with the intensity versus frequency graph ( [link] of the human ear?

Calculate the first overtone in an ear canal, which resonates like a 2.40-cm-long tube closed at one end, by taking air temperature to be $\mathrm{37.0ºC}$ . Is the ear particularly sensitive to such a frequency? (The resonances of the ear canal are complicated by its nonuniform shape, which we shall ignore.)

A crude approximation of voice production is to consider the breathing passages and mouth to be a resonating tube closed at one end. (See [link] .) (a) What is the fundamental frequency if the tube is 0.240-m long, by taking air temperature to be $\mathrm{37.0ºC}$ ? (b) What would this frequency become if the person replaced the air with helium? Assume the same temperature dependence for helium as for air.

(a) Students in a physics lab are asked to find the length of an air column in a tube closed at one end that has a fundamental frequency of 256 Hz. They hold the tube vertically and fill it with water to the top, then lower the water while a 256-Hz tuning fork is rung and listen for the first resonance. What is the air temperature if the resonance occurs for a length of 0.336 m? (b) At what length will they observe the second resonance (first overtone)?

What frequencies will a 1.80-m-long tube produce in the audible range at $\mathrm{20.0ºC}$ if: (a) The tube is closed at one end? (b) It is open at both ends?