The wavelength of a sound wave can be calculated using the formula:
wavelength = velocity / frequency
For the stationary source, the wavelength is:
wavelength = 1125 ft/s / 100 Hz = 11.25 ft
For the person in the car, we need to take into account the relative motion between the car and the sound source. The perceived frequency will be higher than the actual frequency, given by:
observed frequency = actual frequency x (velocity of sound + velocity of observer) / (velocity of sound)
Plugging in the values, we get:
observed frequency = 100 Hz x (1125 ft/s + 200 ft/s) / (1125 ft/s) = 106.67 Hz
Using the observed frequency, we can calculate the perceived wavelength:
perceived wavelength = velocity / observed frequency
perceived wavelength = 1125 ft/s / 106.67 Hz = 10.53 ft
Therefore, the correct option is:
b) wavelength of the stationary source: 11.25 ft; perceived wavelength: 10.53 ft
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?
Which of the following is the best option?
a) wavelength of the stationary source: 11.25 ft; perceived wavelength: 13.25 ft
b) wavelength of the stationary source: 9.25 ft; perceived wavelength: 11.25 ft
c) wavelength of the stationary source: 11.25 ft; perceived wavelength: 9.25 ft
d) wavelength of the stationary source: 13.25 ft; perceived wavelength: 11.25 ft
1 answer