Physic Labs

Problem 3

A fixed loudspeaker emits sound of frequency f=680f=680 Hz in still air, where the sound speed is v=340v=340 m/s. A runner moves directly toward the speaker at vo=20v_o=20 m/s; after passing it, the runner recedes at the same speed. For nonrelativistic Doppler shifts in still air, use f′=(v±vo)f/vf'=(v\pm v_o)f/v for a stationary source and f′=fv/(v∓vs)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 vs=17v_s=17 m/s toward a stationary observer; find the observed frequency.
problems.proof.stepOf
problems.proof.prevStepproblems.proof.nextStep
vrel=v+20=360 m/s (approach),vrel=v−20=320 m/s (recede)v_{\text{rel}}=v+20=360\ \mathrm{m/s}\ (\text{approach}),\quad v_{\text{rel}}=v-20=320\ \mathrm{m/s}\ (\text{recede})
problems.proof.analysis

In the observer frame the sound still has 0.5000.500 m spacing, but wavefronts sweep past at different relative speeds. Dividing those speeds by the wavelength recovers the two frequencies already found.