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{far}}=\frac{v-v_o}{v}f=\frac{320}{340}(680)=640\ \mathrm{Hz}

problems.proof.analysis

After passing the speaker, the runner moves with the incoming wavefronts, lowering the relative meeting speed. The observer receding case uses the minus sign.