Problem 3

A fixed loudspeaker emits sound of frequency

f=680

Hz in still air, where the sound speed is

v=340

m/s. A runner moves directly toward the speaker at

v_o=20

m/s; after passing it, the runner recedes at the same speed. For nonrelativistic Doppler shifts in still air, use

f'=(v\pm v_o)f/v

for a stationary source and

f'=fv/(v\mp v_s)

for a stationary observer. (a) Find the frequencies heard while approaching and receding. (b) Find the wavelength the runner encounters in each case. (c) Now the source moves at

v_s=17

m/s toward a stationary observer; find the observed frequency.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

f'_{\text{source}}=\frac{v}{v-v_s}f=\frac{340}{323}(680)=716\ \mathrm{Hz}

problems.proof.analysis

When the source approaches, wavefronts are compressed in air, shortening the wavelength. For a stationary observer the frequency ahead of the source is multiplied by $v/(v-v_s)$ .