Chapter 12

Problem 46

A ship mapping the depth of the ocean emits a sound of $38 \mathrm{kHz}$. The sound travels to the ocean floor and returns $0.68 \mathrm{s}$ later. (a) How deep is the water at that location? (b) What is the wavelength of the wave in water? (c) What is the wavelength of the reflected wave as it travels into the air, where the speed of sound is $350 \mathrm{m} / \mathrm{s} ?$

Problem 48

A geological survey ship mapping the floor of the ocean sends sound pulses down from the surface and measures the time taken for the echo to return. How deep is the ocean at a point where the echo time (down and back) is $7.07 \mathrm{s} ?$ The temperature of the seawater is $25^{\circ} \mathrm{C}$

Problem 49

A bat emits chirping sounds of frequency $82.0 \mathrm{kHz}$ while hunting for moths to eat. If the bat is flying toward the moth at a speed of $4.40 \mathrm{m} / \mathrm{s}$ and the moth is flying away from the bat at $1.20 \mathrm{m} / \mathrm{s},$ what is the frequency of the sound wave reflected from the moth as observed by the bat? Assume it is a cool night with a temperature of $10.0^{\circ} \mathrm{C} .$ [Hint: There are two Doppler shifts. Think of the moth as a receiver, which then becomes a source as it "retransmits" the reflected wave. $]$

Problem 51

Doppler ultrasound is used to measure the speed of blood flow (see Problem 42). The reflected sound interferes with the emitted sound, producing beats. If the speed of red blood cells is $0.10 \mathrm{m} / \mathrm{s},$ the ultrasound frequency used is $5.0 \mathrm{MHz},$ and the speed of sound in blood is $1570 \mathrm{m} / \mathrm{s},$ what is the beat frequency?

Problem 53

A 30.0 -cm-long string has a mass of $0.230 \mathrm{g}$ and is vibrating at its next-to-lowest natural frequency $f_{2} .$ The tension in the string is $7.00 \mathrm{N} .$ (a) What is $f_{2} ?$ (b) What are the frequency and wavelength of the sound in the surrounding air if the speed of sound is $350 \mathrm{m} / \mathrm{s} ?$

Problem 55

What are the four lowest standing wave frequencies for an organ pipe that is $4.80 \mathrm{m}$ long and closed at one end?

Problem 56

The length of the auditory canal in humans averages about $2.5 \mathrm{cm} .$ What are the lowest three standing wave frequencies for a pipe of this length open at one end? What effect might resonance have on the sensitivity of the ear at various frequencies? (Refer to Fig. 12.12 Note that frequencies critical to specch recognition are in the range 2 to $5 \mathrm{kHz}$ )

Problem 57

Some bats determine their distance to an object by detecting the difference in intensity between cchoes.(a) If intensity falls off at a rate that is inversely proportional to the distance squared, show that the echo intensity is inversely proportional to the fourth power of distance. (b) The bat was originally $0.60 \mathrm{m}$ from one object and $1.10 \mathrm{m}$ from another. After flying closer, it is now $0.50 \mathrm{m}$ from the first and at $1.00 \mathrm{m}$ from the second object. What is the percentage increase in the intensity of the ccho from each object?

Problem 58

The Vespertilionidae family of bats detect the distance to an object by timing how long it takes for an emitted signal to reflect off the object and return. Typically they emit sound pulses 3 ms long and 70 ms apart while cruising. (a) If an echo is heard 60 ms later $\left(v_{\text {sound }}=331 \mathrm{m} / \mathrm{s}\right),$ how far away is the object? (b) When an object is only $30 \mathrm{cm}$ away, how long will it be before the echo is heard? (c) Will the bat be able to detect this echo?

Problem 59

At what frequency $f$ does a sound wave in air have a wavelength of $15 \mathrm{cm},$ about half the diameter of the human head? Some methods of localization work well only for frequencies below $f$, while others work well only above $f$. (See Conceptual Questions 4 and 5 .)