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

\lambda=v/f=340/680=0.500\ \mathrm m\quad\text{(vẫn trong cả hai trường hợp)}

problems.proof.analysis

A stationary source emits crests at the fixed spatial separation $v/f$ . The observer's motion changes only the meeting rate, not the wavelength carried by the medium.

problems.proof.pitfall. Do not compute the air wavelength from the relative speed

v+v_o

divided by

f'

; the medium wavelength is fixed by source and medium alone.