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)
A) wavelength of the stationary source: 11.25 ft; perceived wavelength: 12.25 ft
B)!wavelength of the stationary source: 11.25 ft; perceived wavelength: 10.25 ft
C) wavelength of the stationary source: 10.25 ft; perceived wavelength: 11.25 ft
D) wavelength of the stationary source: 12.25 ft; perceived wavelength: 11.25 ft
First, let's calculate the wavelength of the stationary source using the formula:
wavelength = speed of sound / frequency
wavelength = 1125 ft/s / 100 Hz
wavelength = 11.25 ft
Now, let's calculate the perceived wavelength by the person in the car. Since the car is moving towards the source, the perceived frequency is higher due to the Doppler effect. The formula for calculating the perceived frequency is:
perceived frequency = (speed of sound + speed of observer) / (speed of sound + speed of source) x actual frequency
perceived frequency = (1125 ft/s + 100 ft/s) / (1125 ft/s) x 100 Hz
perceived frequency = 1225 ft/s / 1125 ft/s x 100 Hz
perceived frequency = 108.89 Hz
Now, we can calculate the perceived wavelength using the perceived frequency:
perceived wavelength = speed of sound / perceived frequency
perceived wavelength = 1125 ft/s / 108.89 Hz
perceived wavelength ≈ 10.32 ft
Therefore, the correct answer is:
C) wavelength of the stationary source: 11.25 ft; perceived wavelength: 10.25 ft