** SOLUTIONS Jaquin’s Sections **
SCI111 Homework Assignment #5

(20 Points Total)

Chapter 5

1. A water wave has a frequency of 6 Hz and a wavelength of 3m.

a. What is the period of these waves?

This is a basic wave structure problem. We need only the relation that links the frequency and period of a wave: .

The period of this wave is 0.167 seconds.

b. What is the wave velocity?

This is a basic wave velocity problem. We need only the relation that links the frequency wavelength and velocity of a wave: .

The velocity of this wave is 18 m/s.

2. The lower limit for human hearing is usually considered to be 20 Hz. What is the corresponding wavelength for this frequency if the air temperature is 20.0 C?

This is a wave velocity problem. We need the relation that links the frequency wavelength and velocity of a wave: . Additionally we need to use the speed of sound in air at 20C : . This velocity works out to be 343 m/s at 20C.

The wavelength of 20 Hz sound waves in 20C air is 17.15 meters.

4. The low range of frequencies used for medical applications is about 1,000,000 Hz. What is the wavelength of this frequency in air?

This is a wave velocity problem just like the previous problem. We need the relation that links the frequency wavelength and velocity of a wave: . Additionally we need to use the speed of sound in air at 20C (assumed temperature) : . This velocity works out to be 343 m/s at 20C.

The wavelength of 1,000,000 Hz sound waves in 20C air is 0.343 millimeters.

5. How much time will elapse between seeing and hearing an even that happens 400.0 m away?

This is a basic . Let’s assume that the air temperature is 20C, so that the speed of sound is the by now familiar 343 m/s. The distance is 400.0 m, so…

The elapsed time between seeing and hearing is 1.17 seconds.

6. An echo bounces from a building exactly 1.00 seconds after you honk your horn. How many feet away is the building if the air temperature is 20.0 C?

This is another basic , but with the “echo” twist. The speed of sound is the by now familiar 343 m/s.

The distance the sound wave traveled in 1 second is 343 meters. However, since the sound echoed off the building the building is only ½ that distance or 171.5 meters away.

In feet (1 m = 3.281 ft) the distance is 563 feet from the building.

7. A submarine sends a sonar signal, which returns from another ship 2.250 s later. How far away is the other ship if the speed of sound in sea water is 1,530.0 m/s?

This is yet another basic , but with the “echo” twist. The speed of sound is the 1,530 m/s.

The distance the sound wave traveled underwater in 2.25 second is 3,344.5 meters. However, since the sound echoed off the ship the ship is only ½ that distance or 1,721 meters away

8. A student clicks underwater clicks two rocks together and makes a sound with a frequency of 600.0 Hz and a wavelength of 2.5 meters. What is the speed of this underwater sound?

Like the first problem assigned, this is a basic wave velocity problem. We need only the relation that links the frequency wavelength and velocity of a wave: .

The velocity of this wave is 1,500 m/s.

9. You see condensed steam expelled from a ship’s whistle 2.5 s before you hear the sound. If the air temperature is 20.0 C, how many meters are you from the ship?

This is again another basic . The speed of sound is the by now familiar 343 m/s in air at 20C. The time is 2.5 s, so…

The ship is 857.5 meters away.

11. A tuning fork vibrates 440.0 times second, producing sound waves with a wavelength of 78.0 cm. What is the velocity of these waves?

This is a straight forward problem.

The velocity of these waves is 343.2 m/s.

12. The distance between the center of a condensation and the center of an adjacent rarefaction is 65.23 cm. If the frequency is 256.0 Hz, how fast are these waves moving?

This is a problem with one complication. We need to recognize that the distance between the center of a condensation and the center of an adjacent rarefaction of 65.23 cm represents only ½.

The velocity of these waves is 334 m/s.

14. Sound from the siren of an emergency vehicle has a frequency of 750.0 Hz and moves with a velocity of 343.0 m/s. What is the distance from one condensation to the next?

This is a straight forward problem where we need to solve for the wavelength  of the sound.

The distance from one condensation to the next is one wavelength and is equal to 0.457 m or 45.7 cm. (Note the units)

15. The following sound waves have what velocity?

a. 20.0 Hz,  of 17.15 m

This is a straight forward problem.

The velocity of these waves is 343 m/s.

b. 200.0 Hz,  of 1.715 m

The velocity of these waves is also 343 m/s.

c. 2,000.0 Hz,  of 17.15 cm

The velocity of these waves is also 343 m/s.

d. 20,000.0 Hz,  of 1.715 cm

The velocity of these waves also 343 m/s.

17. A ship at sea sounds a whistle blast, and an echo returns from the coastal land 10.0 s later. How many km is it to the coastal land if the air temperature s 10.0C?

This is a problem where we first need to determine the speed of sound in air at 10C.

The whistle blast travels a total distance of 3, 370 meters. Therefore the distance form the land mass is ½ that distance or 1.685 kilometers.

19. A 600.0 Hz sound has a velocity of 1,087 ft/s in the air and a velocity of 4,920.0 ft/s in water. Find the wavelength of this sound in (a) the air and (b) the water.

This is a straight forward problem where we need to solve for the wavelength  of the sound.

The wavelength of this sound in the air is 1.81 feet and in the water is 8.20 feet.