Question

A car horn emits a frequency of 400 Hz. A car traveling at 20.0 m/s sounds the horn as it approaches a stationary pedestrian. What frequency does the pedestrian hear

Answer 1

The observed frequency by the pedestrian is 424 Hz.

Step-by-step explanation:

Given;

frequency of the source, Fs = 400 Hz

speed of the car as it approaches the stationary observer, Vs = 20 m/s

Based on Doppler effect, as the car the approaches the stationary observer, the observed frequency will be higher than the transmitted (source) frequency because of decrease in distance between the car and the observer.

The observed frequency is calculated as;

`F_s = F_o [(v)/(v_s + v) ] \\\\`

where;

F₀ is the observed frequency

v is the speed of sound in air = 340 m/s

`F_s = F_o [(v)/(v_s + v) ] \\\\400 = F_o [(340)/(20 + 340) ] \\\\400 = F_o (0.9444) \\\\F_o = (400)/(0.9444) \\\\F_o = 423.55 \ Hz \\`

F₀ ≅ 424 Hz.

Therefore, the observed frequency by the pedestrian is 424 Hz.