In this worksheet, we will practice relating the temperature of a gas in which sound waves propagate to the propagation speed of the waves.

**Q5: **

A bat uses sound waves of frequency Hz to locate insects. If the sound waves travel through air at a speed of 343 m/s, what is the wavelength of the sound waves?

**Q6: **

Ultrasound equipment used in the medical profession uses sound waves of a frequency above the range of human hearing. If the frequency of the sound produced by the ultrasound machine is 30 kHz, what is the wavelength of the ultrasound in bone, if the speed of sound in bone is m/s?

**Q7: **

Consider a diagnostic ultrasound of frequency 5.00 MHz that is used to examine an irregularity in soft tissue.

What is the wavelength in air of such a sound wave if the speed of sound is 343 m/s?

If the speed of sound in tissue is m/s, what is the wavelength of this wave in tissue?

**Q8: **

A quality assurance engineer at a frying pan company is asked to qualify a new line of nonstick-coated frying pans. The coating needs to be 1.00 mm thick. One method to test the thickness is for the engineer to pick a percentage of the pans manufactured, strip off the coating, and measure the thickness using a micrometer. This method is a destructive testing method. Instead, the engineer decides that every frying pan will be tested using a nondestructive method. An ultrasonic transducer is used that produces sound waves with a frequency of kHz. The sound waves are sent through the coating and are reflected by the interface between the coating and the metal pan, and the time is recorded. The wavelength of the ultrasonic waves in the coating is 0.0760 mm. What should be the time recorded if the coating is the correct thickness?

**Q9: **

How many times greater is the frequency of a sound wave generated by the vibration of a wind instrument in air at a temperature of than in air at a temperature of ?

**Q10: **

A bat detects the reflected sound of its cries to locate its insect prey, 3.00 m away.

Calculate the time interval between the bat emitting a cry and detecting its reflection. Assume an air temperature of 5.0℃.

Calculate the time interval between the bat emitting a cry and detecting its reflection. Assume an air temperature of 35℃.

What is the percent uncertainty in the time interval between the bat emitting a cry and detecting its reflection that is produced by a change in air temperature of 30℃?

**Q11: **

A tuning fork of frequency 110 Hz is struck and begins to vibrate. A sound level meter is located 17 m away. It takes the sound 0.25 s to reach the meter. What is the wave number of the sound wave produced by the tuning fork?

**Q12: **

Dolphins emit sound waves that they use for communication. If the wavelength of an emitted sound wave is 3.0 cm and the speed of sound in the medium is m/s, what is the period of the sound wave?

- A s
- B s
- C s
- D s
- E s

**Q13: **

A dolphin makes sounds in air and in seawater. Given that the temperature of
air is , what is the ratio of the wavelength of a sound in air to its wavelength
in seawater? Use a value of 1.225 kg/m^{3} for the density of air
and kg/m^{3} for the density of seawater.

**Q14: **

A bat emits a sound wave of frequency 87 kHz and sound waves travel through air at a speed of 343 m/s.

What is the period of the wave?

- A s
- B s
- C s
- D s
- E s

What is the wavelength of the sound wave?

- A m
- B m
- C m
- D m
- E m

**Q15: **

What is the speed of a sound wave that has a frequency of Hz and a wavelength of 0.256 m?

**Q16: **

The density of a sample of a certain fluid is
kg/m^{3} and
the sample’s bulk modulus
is 3.650 GPa. What
is the speed of sound through the sample?

**Q17: **

A submarine’s sonar can measure echo times with a precision of
0.001000 s.
Determine the smallest difference in positions that the sonar can be used to detect.
Use a value of kg/m^{3}
for the density of water and use a value of 2.340 GPa for the bulk modulus of water.

**Q18: **

A woman emits a shriek of frequency Hz. Find the wavelength of the sound wave produced. Use a value of 342 m/s for the speed of sound.

**Q19: **

The cross section of a 10.0-meter-long steel I-beam is shown in the accompanying diagram. The weight of the I-beam is N. What would be the speed of sound in the I-beam? Use 200 GPa as the bulk modulus of elasticity of steel.

**Q20: **

A physicist at a fireworks display times the lag between seeing an explosion and hearing its sound and finds it to be 0.840 s. The air temperature in the region of the fireworks display is .

How far away is the explosion, neglecting the time taken for light to reach the physicist?

Find the difference between the distance to the explosion found with and without taking the speed of light into account.

- A m
- B m
- C m
- D m
- E m

**Q21: **

The speed of sound in an ideal gas at temperature of 200 K is 100 m/s. What is the speed of sound of the same gas at a temperature of 800 K?

**Q22: **

Calculate the speed of sound in an ideal gas at a temperature of 273 K.

**Q23: **

What is the wavelength of an earthquake that has a frequency of 9.00 Hz and travels 82.0 km in 20.0 s?

**Q24: **

Your ear is capable of differentiating sounds that arrive at each ear just 0.34 ms apart, which is useful in determining where low-frequency sounds are originating from. A low-frequency sound source is placed to the right of a person whose ears are approximately mm apart, and the speed of the sound generated is 340 m/s.

How long is the interval between the sound arriving at the right ear and the sound arriving at the left ear?

Assume the same person was scuba diving and a low-frequency sound source was to the right of the scuba diver. Determine the interval between the arrival of the sound at the right ear and at the left ear. Use a value of m/s for the speed of sound in water.

**Q25: **

A Girl Scout is hiking a distance of 8.00 km to earn a merit badge. While on the hike, she sees a cliff some distance away. She wishes to estimate the time required to walk to the cliff. She assumes that the speed of sound is 343 meters per second. She yells and finds that the echo returns after 2.50 seconds. If she can hike 1.00 km in 15 minutes, how long would it take her to reach the cliff?