第17章音

(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?

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?

The ear canal resonates like a tube closed at one end. (See Figure 17.14.) 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 $37.0\text{°}\text{C,}$ which is the same as body temperature.

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 $37.0\text{°}\text{C}$. 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. (a) What is the fundamental frequency if the tube is 0.240 m long, by taking air temperature to be $37.0\text{°}\text{C}$? (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 4.0-m-long pipe, open at one end and closed at one end, is in a room where the temperature is $T=22\text{°}\text{C}\text{.}$ A speaker capable of producing variable frequencies is placed at the open end and is used to cause the tube to resonate. (a) What is the wavelength and the frequency of the fundamental frequency? (b) What is the frequency and wavelength of the first overtone?

A 4.0-m-long pipe, open at both ends, is placed in a room where the temperature is$T=25\text{°}\text{C}\text{.}$ A speaker capable of producing variable frequencies is placed at the open end and is used to cause the tube to resonate. (a) What are the wavelength and the frequency of the fundamental frequency? (b) What are the frequency and wavelength of the first overtone?

A nylon guitar string is fixed between two lab posts 2.00 m apart. The string has a linear mass density of $\mu =7.20\text{g/m}$ and is placed under a tension of 160.00 N. The string is placed next to a tube, open at both ends, of length L. The string is plucked and resonates at the fundamental frequency while the tube resonates at the $n=3$ mode. The speed of sound is 343 m/s. What is the length of the tube?

A 512-Hz tuning fork is struck and placed next to a tube with a movable piston, creating a tube with a variable length. The piston is slid down the pipe and resonance is reached when the piston is 115.50 cm from the open end. The next resonance is reached when the piston is 82.50 cm from the open end. (a) What is the speed of sound in the tube? (b) How far from the open end will the piston cause the next mode of resonance?

Students in a physics lab are asked to find the length of an air column. They obtain a long tube that is 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. (a) 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)?