A small musical toy produces a steady tone at $1000 \mathrm{~Hz}$. It is accidentally dropped from the window of a tall apartment building. How far has it fallen if the frequency heard from the window is $950 \mathrm{~Hz}$ ? (Ignore air friction, and use $340 \mathrm{~m} / \mathrm{s}$ for the speed of sound.)

A young person with normal hearing can hear sounds ranging from $20 Hz$ to $20 kHz$. How many octaves can such a person hear? (Recall that if two tones differ by an octave, the higher frequency is twice the lower frequency.)

The sound source of a ship's sonar system operates at a frequency of $22.0 \mathrm{kHz}$. The speed of sound in water (assumed to be at a uniform $20^{\circ} \mathrm{C}$ ) is $1482 \mathrm{~m} / \mathrm{s}$. $(a)$ What is the wavelength of the waves emitted by the source? $(b)$ What is the difference in frequency between the directly radiated waves and the waves reflected from a whale traveling directly toward the ship at $4.95 \mathrm{~m} / \mathrm{s}$ ? The ship is at rest in the water.

A bat flies toward a wall, emitting a steady sound of frequency $2000 \mathrm{~Hz}$. The bat hears its own sound, plus the sound reflected by the wall. How fast should the bat fly in order to hear a beat frequency of $10.0 \mathrm{~Hz}$? (Hint: Break this problem into two parts, first with the bat as the source and the wall as the listener, and then with the wall as the source and the bat as the listener.)

A musician tunes the $\mathrm{C}$-string of her instrument to a fundamental frequency of $65.4 \mathrm{~Hz}$. The vibrating portion of the string is $0.600$ m long and has a mass of $14.4 \mathrm{~g}$.
(b) What percent increase in tension is needed to increase the fre- quency from $65.4 \mathrm{~Hz}$ to $73.4 \mathrm{~Hz}$, corresponding to a rise in pitch from $C$ to $D$?

A musician tunes the C-string of her instrument to a fundamental frequency of 65.4 Hz. The vibrating portion of the string is 0.600 m long and has a mass of 14.4 g.

With what tension must the musician stretch it?

A very noisy chain saw operated by a tree surgeon emits a total acoustic power of $20.0 \mathrm{~W}$ uniformly in all directions. At what distance from the source is the sound level equal to
(a) $100 \mathrm{~dB}$,
(b) $60 \mathrm{~dB}$ ?

A $2.00 \mathrm{MHz}$ sound wave travels through a pregnant woman's abdomen and is reflected from the fetal heart wall of her unborn baby. The heart wall is moving toward the sound receiver as the heart beats. The reflected sound is then mixed with the transmitted sound, and $85$ beats per second are detected. The speed of sound in body tissue is $1500 \mathrm{~m} / \mathrm{s}$. Calculate the speed of the fetal heart wall at the instant this measurement is made.

One end of a $14.0$-m-long wire having a total mass of $0.800 \mathrm{~kg}$ is fastened to a fixed support in the ceiling, and a $7.50 \mathrm{~kg}$ object is hung from the other end. If the wire is struck a transverse blow at one end, how much time does the pulse take to reach the other end? Neglect the variation in tension along the length of the wire.

When a $15 \mathrm{~kg}$ mass is hung vertically from a thin, light wire, pulses take time $t$ to travel the full length of the wire. If an additional $15 \mathrm{~kg}$ mass is added to the first one without changing the length of the wire, the time taken for pulses to travel the length of the wire will be
A. $2 t$.
B. $\sqrt{2} t$.
C. $t / 2$.
D. $t / \sqrt{2}$.

Lane dividers on highways sometimes have regularly spaced ridges or ripples. When the tires of a moving car roll along such a divider, a musical note is produced. Why? Explain how this phenomenon could be used to measure the car’s speed.

Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s. How fast (as a percentage of light speed) would a star have to be moving so that the frequency of the light we receive from it is 10.0% higher than the frequency of the light it is emitting? Would it be moving away from us or toward us? (Assume it is moving either directly away from us or directly toward us.)

Suppose instead that the source is stationary and the listener moves toward the source at one-half the speed of sound. What frequency does the listener hear? How does your answer compare to that in part (a)? Explain on physical grounds why the two answers differ.

While sitting in your car by the side of a country road, you see your friend, who happens to have an identical car with an identical horn, approaching you. You blow your horn, which has a frequency of $260 \mathrm{~Hz}$; your friend begins to blow his horn as well, and you hear a beat frequency of $6.0 \mathrm{~Hz}$. How fast is your friend approaching you?