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.

Horseshoe bats (genus Rhinolophus) emit sounds from their nostrils and then listen to the frequency of the sound reflected from their prey to determine the prey’s speed. (The “horseshoe” that gives the bat its name is a depression around the nostrils that acts like a focusing mirror, so that the bat emits sound in a narrow beam like a flashlight.) A Rhinolophus flying at speed $\mathrm{v}_{\mathrm{bat}}$ emits sound of frequency $\mathrm{f}_{\mathrm{bat}}$; the sound it hears reflected from an insect flying toward it has a higher frequency $\mathrm{f}_{\mathrm{refl}}$.

If $\mathrm{f}_{\mathrm{bat}}=80.7 \mathrm{kHz}$, $f_{\text { refl }}=83.5 \mathrm{kHz}$, and $v_{\text { bat }}=3.9 \mathrm{m} / \mathrm{s}$, calculate the speed of the insect.

The sound source of a ship's sonar system operates at a frequency of $18.0 \mathrm{kHz}$. The speed of sound in water (assumed to be at a uniform $20\degree$C) is $1482$ m$/$s.
(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 $4.95$ m$/$s? The ship is at rest in the water.

The sound source of a ship’s sonar system operates at a frequency of 18.0 kHz. The speed of sound in water (assumed to be at a uniform $20^{\circ} \mathrm{C}$) is 1482 m/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 m/s? The ship is at rest in the water.

Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s. A stationary police car emits a sound of frequency 1200 Hz that bounces off a car on the highway and returns with a frequency of 1250 Hz. The police car is right next to the highway, so the moving car is traveling directly toward or away from it. (a) How fast was the moving car going? Was it moving toward or away from the police car? (b) What frequency would the police car have received if it had been traveling toward the other car at 20.0 m/s?

A stationary police car emits a sound of frequency $1200 \mathrm{~Hz}$ that bounces off a car on the highway and returns with a frequency of $1250 \mathrm{~Hz}$. The police car is right next to the high- way, so the moving car is traveling directly toward or away from it.
(b) What frequency would the police car have received if it had been traveling toward the other car at $20.0$ m$/$s?

A stationary police car emits a sound of frequency $1200 \mathrm{~Hz}$ that bounces off of a car on the highway and returns with a frequency of $1250 \mathrm{~Hz}$. The police car is right next to the highway, so the moving car is traveling directly toward or away from it.
(a) How fast was the moving car going? Was it moving towards or away from the police car?
(b) What frequency would the police car have received if it had been traveling toward the other car at $20.0 \mathrm{~m} / \mathrm{s}$?

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?

The listener moves at $80 \mathrm{~m} / \mathrm{s}$ relative to still air toward the stationary source. (a) What is the wavelength of the sound in the region between the source and the listener? (b) What is the frequency heard by the listener?

A source of sound waves of frequency 1.0 kHz is traveling thorough the air at 0.50 times the speed of sound. (a) Find the frequency of the sound received by a stationary observer if the source moves toward her. (b) Repeat if the source moves away from her instead.

A source of sound waves of frequency 1.0 kHz is stationary. An observer is traveling at 0.50 times the speed of sound. (a) What is the observed frequency if the observer moves toward the source? (b) Repeat if the observer moves away from the source instead.

An enemy spaceship, which is moving at high speed away from the planet Anakin, fires a rocket toward the planet with a speed of $0.920 c$ relative to the spaceship. (See Figure 27.25.) A commander on Arrakis reports that the rocket is approaching with a speed of $0.360 c$. What is the speed of the spaceship relative to Arrakis?

The fundamental frequency of the longest pipe on an organ is 16.35 Hz. If the pipe is open at both ends, how long is the pipe?

Loudspeakers A and B are 7 m apart and vibrate in phase at 172 Hz. They radiate sound uniformly in all directions. Their acoustic power outputs are $8.00 \times 10^{-4} \mathrm{~W}$ and $6.00 \times 10^{-5} \mathrm{~W}$, respectively. The air temperature is $20^{\circ} \mathrm{C}$. Determine the difference in phase of the two signals at a point $C$ along the line joining $A$ and $B, 3.00 \mathrm{~m}$ from $B$ and $4.00 \mathrm{~m}$ from A.

Choose the equations that relate power, distance from the source, intensity, pressure amplitude, and sound intensity level.