第17章音

A 0.80-m-long tube is opened at both ends. The air temperature is $26\text{°}\text{C}\text{.}$ The air in the tube is oscillated using a speaker attached to a signal generator. What are the wavelengths and frequencies of first two modes of sound waves that resonate in the tube?

A tube filled with water has a valve at the bottom to allow the water to flow out of the tube. As the water is emptied from the tube, the length L of the air column changes. A 1024-Hz tuning fork is placed at the opening of the tube. Water is removed from the tube until the $n=5$ mode of a sound wave resonates. What is the length of the air column if the temperature of the air in the room is $18\text{°}\text{C?}$

Consider the following figure. The length of the string between the string vibrator and the pulley is $L=1.00\text{m}\text{.}$ The linear density of the string is $\mu =0.006\text{kg/m}\text{.}$ The string vibrator can oscillate at any frequency. The hanging mass is 2.00 kg. (a)What are the wavelength and frequency of $n=6$ mode? (b) The string oscillates the air around the string. What is the wavelength of the sound if the speed of the sound is $v_s=343.00\text{m/s}$?

Early Doppler shift experiments were conducted using a band playing music on a train. A trumpet player on a moving railroad flatcar plays a 320-Hz note. The sound waves heard by a stationary observer on a train platform hears a frequency of 350 Hz. What is the flatcar’s speed in mph? The temperature of the air is $T_{\text{C}}=22\text{°}\text{C}$.

Two cars move toward one another, both sounding their horns $\left(f_s=800\text{Hz}\right)$. Car A is moving at 65 mph and Car B is at 75 mph. What is the beat frequency heard by each driver? The air temperature is $T_C=22.00\text{°}\text{C}$.

Student A runs after Student B. Student A carries a tuning fork ringing at 1024 Hz, and student B carries a tuning fork ringing at 1000 Hz. Student A is running at a speed of $v_A=5.00\text{m/s}$ and Student B is running at $v_B=6.00\text{m/s}\text{.}$ What is the beat frequency heard by each student? The speed of sound is $v=343.00\text{m/s}\text{.}$

Suppose that the sound level from a source is 75 dB and then drops to 52 dB, with a frequency of 600 Hz. Determine the (a) initial and (b) final sound intensities and the (c) initial and (d) final sound wave amplitudes. The air temperature is $T_{\text{C}}=24.00\text{°}\text{C}$ and the air density is $\rho =1.184{\text{kg/m}}^3.$

The Doppler shift for a Doppler radar is found by $f=f_R\left(\frac{1+\frac{v}{c}}{1-\frac{v}{c}}\right)$, where $f_R$ is the frequency of the radar, f is the frequency observed by the radar, c is the speed of light, and v is the speed of the target. What is the beat frequency observed at the radar, assuming the speed of the target is much slower than the speed of light?

A stationary observer hears a frequency of 1000.00 Hz as a source approaches and a frequency of 850.00 Hz as a source departs. The source moves at a constant velocity of 75 mph. What is the temperature of the air?

A flute plays a note with a frequency of 600 Hz. The flute can be modeled as a pipe open at both ends, where the flute player changes the length with his finger positions. What is the length of the tube if this is the fundamental frequency?

Two sound speakers are separated by a distance d, each sounding a frequency f. An observer stands at one speaker and walks in a straight line a distance x, perpendicular to the the two speakers, until he comes to the first maximum intensity of sound. The speed of sound is v. How far is he from the speaker? Assume the distance, d, between the slits is larger than the wavelength of the sound.

Consider the beats shown below. This is a graph of the gauge pressure versus time for the position $x=0.00\text{m}\text{.}$ The wave moves with a speed of $v=343.00\text{m/s}\text{.}$ (a) How many beats are there per second? (b) How many times does the wave oscillate per second? (c) Write a wave function for the gauge pressure as a function of time.

Two speakers producing the same frequency of sound are a distance of d apart. Consider an arc along a circle of radius R, centered at the midpoint of the speakers, as shown below. (a) At what angles will there be maxima? (b) At what angle will there be minima?

A string has a length of 1.5 m, a linear mass density $\mu =0.008\text{kg/m,}$, and a tension of 120 N. If the air temperature is $T=22\text{°}\text{C,}$ what should the length of a pipe open at both ends for it to have the same frequency for the $n=3$ mode?

A string $\left(\mu =0.006\frac{\text{kg}}{\text{m}},L=1.50\text{m}\right)$ is fixed at both ends and is under a tension of 155 N. It oscillates in the $n=10$ mode and produces sound. A tuning fork is ringing nearby, producing a beat frequency of 23.76 Hz. (a) What is the frequency of the sound from the string? (b) What is the frequency of the tuning fork if the tuning fork frequency is lower? (c) What should be the tension of the string for the beat frequency to be zero?

A string has a linear mass density $\mu$, a length L, and a tension of $F_T$, and oscillates in a mode n at a frequency f. Find the ratio of $\frac{\text{Δ}f}{f}$ for a small change in tension.

A string has a linear mass density $\mu =0.007\text{kg/m,}$ a length $L=0.70\text{m,}$ a tension of $F_T=110\text{N},$ and oscillates in a mode $n=3$. (a) What is the frequency of the oscillations? (b) Use the result in the preceding problem to find the change in the frequency when the tension is increased by $1.00\text{\%}$.

A speaker powered by a signal generator is used to study resonance in a tube. The signal generator can be adjusted from a frequency of 1000 Hz to 1800 Hz. First, a 0.75-m-long tube, open at both ends, is studied. The temperature in the room is $T_{\text{F}}=85.00\text{°}\text{F}\text{.}$ (a) Which normal modes of the pipe can be studied? What are the frequencies and wavelengths? Next a cap is place on one end of the 0.75-meter-long pipe. (b) Which normal modes of the pipe can be studied? What are the frequencies and wavelengths?

A string on the violin has a length of 23.00 cm and a mass of 0.900 grams. The tension in the string 850.00 N. The temperature in the room is $T_C=24.00\text{°}\text{C}\text{.}$ The string is plucked and oscillates in the $n=9$ mode. (a) What is the speed of the wave on the string? (b) What is the wavelength of the sounding wave produced? (c) What is the frequency of the oscillating string? (d) What is the frequency of the sound produced? (e) What is the wavelength of the sound produced?