A stationary source produces a sound wave at a frequency of 100 Hz. The wave travels at 1125 feet per second. A car is moving toward the sound source at a speed of 100 feet per second.
What is the wavelength of the stationary sound source and the wavelength that a person in the car perceives?
• wavelength of the stationary source: 12.25 ft; perceived wavelength: 11.25 ft
• wavelength of the stationary source: 11.25 ft; perceived wavelength: 12.25 ft
• wavelength of the stationary source: 10.25 ft; perceived wavelength: 11.25 ft
• wavelength of the stationary source: 11.25 ft; perceived wavelength: 10.25 ft
To find the wavelength of the stationary sound source, we can use the formula:
wavelength = velocity / frequency
wavelength = 1125 ft/s / 100 Hz
wavelength = 11.25 ft
To find the wavelength perceived by a person in the car, we need to account for the Doppler effect. The observed frequency (f') can be calculated using the formula:
f' = f (v + v_0) / (v + v_s)
where:
f = frequency of the stationary source
v = velocity of sound
v_0 = velocity of the observer
v_s = velocity of the source
Substitute the given values:
f' = 100 Hz (1125 ft/s + 100 ft/s) / (1125 ft/s - 100 ft/s)
f' = 110,625 / 1025
f' = 107.80 Hz
The perceived wavelength can then be calculated using the observed frequency:
wavelength = velocity / frequency
wavelength = 1125 ft/s / 107.80 Hz
wavelength = 10.45 ft
Therefore, the correct answer is:
- wavelength of the stationary source: 11.25 ft
- perceived wavelength: 10.45 ft