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: 12.25 ft; perceived wavelength: 11.25 ft
wavelength of the stationary source: 12.25 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: 10.25 ft; perceived wavelength: 11.25 ftA 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: 11.25 ft; perceived wavelength: 12.25 ft
wavelength of the stationary source: 12.25 ft; perceived wavelength: 11.25 ft
wavelength of the stationary source: 11.25 ft; perceived wavelength: 10.25 ft
wavelength of the stationary source: 10.25 ft; perceived wavelength: 11.25 ft
The correct response is: wavelength of the stationary source: 11.25 ft; perceived wavelength: 12.25 ft.
To find the wavelength of the stationary source, we use the formula wavelength = speed of sound / frequency:
wavelength = 1125 ft/s / 100 Hz = 11.25 ft
To find the perceived wavelength by a person in the car, we use the formula: perceived wavelength = (speed of sound - speed of listener) / frequency:
perceived wavelength = (1125 ft/s - 100 ft/s) / 100 Hz = 12.25 ft.
To find the wavelength of the stationary sound source, we can use the formula:
\[v = f \lambda\]
where \(v\) is the velocity of the wave, \(f\) is the frequency, and \(\lambda\) is the wavelength.
Given that the wave travels at 1125 feet per second and the frequency is 100 Hz, we can calculate the wavelength of the stationary sound source:
\[\lambda = \frac{v}{f} = \frac{1125}{100} = 11.25 \text{ ft}\]
So the wavelength of the stationary sound source is 11.25 ft.
To find the perceived wavelength by a person in the moving car, we need to consider the Doppler effect. The perceived frequency (\(f'\)) can be calculated using the formula:
\[f' = \frac{v + v_o}{v + v_s} f\]
where \(v_o\) is the velocity of the observer (person in the car), \(v_s\) is the velocity of the source (stationary source), and \(f\) is the frequency.
Given that the car is moving toward the sound source at a speed of 100 feet per second, the perceived wavelength by a person in the car can be calculated using:
\[\lambda' = \frac{v}{f'} = \frac{1125}{\frac{1125 + 100}{1125}} = 12.25 \text{ ft}\]
So the perceived wavelength by a person in the car is 12.25 ft.
Therefore, the correct answer is:
wavelength of the stationary source: 11.25 ft; perceived wavelength: 12.25 ft