Sound Wave Phenomena Quick Check
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Question
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?
(1 point)
Responses
wavelength of the stationary source: 11.25 ft; perceived wavelength: 12.25 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: 10.25 ft; perceived wavelength: 11.25 ft
wavelength of the stationary source: 11.25 ft; perceived wavelength: 10.25 ft
wavelength of the stationary source: 11.25 ft; perceived wavelength: 10.25 ft
wavelength of the stationary source: 12.25 ft; perceived wavelength: 11.25 ft
Correct response: wavelength of the stationary source: 11.25 ft; perceived wavelength: 10.25 ft
Explanation: The wavelength of the sound can be calculated using the equation wavelength = speed of sound / frequency. For the stationary source, the wavelength is 1125 ft/s / 100 Hz = 11.25 ft.
For the perceived wavelength by the person in the car, you would need to take into account the Doppler effect. Since the car is moving towards the source, the perceived frequency will be higher. The equation for the perceived frequency is given by:
f' = f * (v + vo) / (v + vs),
Where f' is the perceived frequency, f is the frequency of the source, v is the speed of sound, vo is the speed of the observer, and vs is the speed of the source.
In this case, the observed frequency is 1125 ft/s / (1125 ft/s + 100 ft/s) * 100 Hz = 10.25 ft. Therefore, the perceived wavelength is 1125 ft/s / 10.25 Hz = 10.25 ft.