Speed of Sound Calculations:
1. Calculate the time it would take for sound to travel through 2000 m of the following
substances, given the velocity of sound through the substance:
a) Helium (972 m/s)
b)Water (1450 m/s)
c) Steel (5130 m/s)
d) Glass (4700 m/s)
2. Calculate the wavelength in the following substances if the frequency is 1000 s-1and the
speed of sound in the medium is given:
a) Lead (1230 m/s)
b) Hydrogen (1267 m/s)
c) Water (5250 km/h)
d) Air (1234 km/h)
3. Calculate the speed of sound in air for the following temperatures:
a) 0°C
b) 25°C
c) 30°C
d) -15°C
4. What is the wavelength of the sound produced by a bat if the frequency of the sound is 90
kHz on a night when the air temperature is 22°C?
5. How far away is a storm if you hear the sound of thunder 7.0 s after the lightning flash on a
day when the air temperature is 31°C?
6. Determine the depth of water if an echo using sonar returns in 870 ms and the speed of
sound in water is 5300 km/h.
7. If it takes 0.8 s for your voice to be heard at a distance of 272 m, what is the temperature of
the air?
8. If you stand on top of a hill overlooking a lake and shout, how long is the lake if an echo is
heard 2.0 s later on a day when the air temperature is 21°C?
9. The air temperature is 20°C. You are swimming underwater when you hear a boat noise.
Then, 3.5 s later, you hear a crash. If the speed of sound in water is 1450 m/s, how long after
the crash does your friend on the dock beside you hear the crash?
10. On a hot summer night (32°C), you are listening to a rock group in a stadium 350 m away. A
friend of yours is sitting in an air-conditioned house across the country, listening to the
broadcast on the radio. If the signal travels 30,000 km up to a satellite that retransmits it, who
hears the concert first (speed of signal = 3.00 x 108 m/s)?
11. How many times more wavelengths occur in air than in water for an air temperature of 10°C
if the speed of sound in water is 5220 km/h and the frequency of sound is 500 Hz?
Mach Number and the Sound Barrier
12. Calculate the Mach number for the following speeds of sound. State whether the speed is
subsonic or supersonic. Assume the speed of sound in air to be 332 m/s:
a) 664 m/s
b) 306 m/s
c) 140 km/h
d) 7171 km/h
13. Calculate the Mach number for sound, given the temperature and the speed:
a) 332 m/s at 30°C
b) 340 m/s at -10°C
c) 6000 km/h at 13°C
d) 6000 km/h at -13°C
14. How far has a plane travelled from the point at which you hear the sound of a sonic boom if
the plane is travelling at Mach 2.2 at an altitude of 8000 m and the average air temperature for
the sound is 15°C?
Answers
1.) 9.) 11.3 s
a. 2.06 s 10.) The person at home
b. 1.379 s 11.) 4.29
c. 0.3899 s 12.)
d. 0.4255 s a. 2.00
2.) b. 0.922
a. 1.230 m c. 0.117
b. 1.267 m d. 6.00
c. 1.458 m 13.)
d. 0.3428 m a. 0.949
3.) b. 1.04
a. 332 m/s c. 4.90
b. 347 m/s d. 5.14
c. 350 m/s 14.) 1.8x104 m
d. 323 m/s
4.) 0.049 m
5.) 2.5 km
6.) 640 m
7.) 13 oC
8.) 3.5x102 m
