### Additional Problems

A 0.80-m-long tube is opened at both ends. The air temperature is $26\text{\xb0}\text{C}\text{.}$ 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 $18\text{\xb0}\text{C?}$

Consider the following figure. The length of the string between the string vibrator and the pulley is $L=1.00\phantom{\rule{0.2em}{0ex}}\text{m}\text{.}$ The linear density of the string is $\mu =0.006\phantom{\rule{0.2em}{0ex}}\text{kg/m}\text{.}$ 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 ${v}_{s}=343.00\phantom{\rule{0.2em}{0ex}}\text{m/s}$?

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 ${T}_{\text{C}}=22\text{\xb0}\text{C}$.

Two cars move toward one another, both sounding their horns $\left({f}_{s}=800\phantom{\rule{0.2em}{0ex}}\text{Hz}\right)$. 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 ${T}_{C}=22.00\text{\xb0}\text{C}$.

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 ${v}_{A}=5.00\phantom{\rule{0.2em}{0ex}}\text{m/s}$ and Student B is running at ${v}_{B}=6.00\phantom{\rule{0.2em}{0ex}}\text{m/s}\text{.}$ What is the beat frequency heard by each student? The speed of sound is $v=343.00\phantom{\rule{0.2em}{0ex}}\text{m/s}\text{.}$

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 ${T}_{\text{C}}=24.00\text{\xb0}\text{C}$ and the air density is $\rho =1.184\phantom{\rule{0.2em}{0ex}}{\text{kg/m}}^{3}.$

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?