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)

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: 12.25 ft; perceived wavelength: 11.25 ft

wavelength of the stationary source: 11.25 ft; perceived wavelength: 10.25 ft

Answer 1

Wavelength of the source: λ = v/f = 1125/100 = 11.25 ft.

Observer moving toward source: f' = f (v + v_o)/v = 100*(1125+100)/1125 = 108.9 Hz (≈108.89 Hz), so λ' = v/f' ≈ 1125/108.9 ≈ 10.3 ft (closest choice 10.25 ft).

Answer: wavelength of the stationary source: 11.25 ft; perceived wavelength: 10.25 ft.