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 200 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: 9.25 ft
wavelength of the stationary source: 11.25 ft; perceived wavelength: 9.25 ft
wavelength of the stationary source: 13.25 ft; perceived wavelength: 11.25 ft
wavelength of the stationary source: 13.25 ft; perceived wavelength: 11.25 ft
wavelength of the stationary source: 11.25 ft; perceived wavelength: 13.25 ft
wavelength of the stationary source: 11.25 ft; perceived wavelength: 13.25 ft
wavelength of the stationary source: 9.25 ft; perceived wavelength: 11.25 ft
wavelength of the stationary source: 11.25 ft; perceived wavelength: 9.25 ft
Explanation:
The wavelength of a sound wave is calculated by dividing the speed of sound by the frequency. For the stationary source, the wavelength is calculated as 1125 ft/s / 100 Hz = 11.25 ft.
For the perceived wavelength by a person in the moving car, you need to take into account the relative motion of the car. The frequency perceived by the person in the car is different due to the Doppler effect. The perceived frequency can be calculated as (speed of sound + speed of car) / (speed of sound / original frequency). In this case, the perceived frequency is (1125 ft/s + 200 ft/s) / (1125 ft/s / 100 Hz) = 9.25 ft. Then, the wavelength can be calculated as the speed of sound / perceived frequency = 1125 ft/s / 9.25 Hz = 9.25 ft.