Understanding Doppler Shifts II

Classical Mechanics Level 2

A buzzer has a center frequency of 400Hz.

We perform two experiments:

(1) A stationary observer on the ground on a windless day hears a Doppler shifted frequency f 1 f_1 from a moving source approaching the observer directly at velocity v.

(2) A moving observer is approaching a stationary buzzer at a velocity of v. The observer will hear a Doppler shifted frequency f 2 f_2 .

Claim: The shifted frequencies f 1 f_1 and f 2 f_2 are exactly IDENTICAL because the relative velocities in both cases are the same!

True or False?

FALSE! TRUE!

Max Yuen by Max Yuen , 42, USA

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1 solution

f 2 f_2 =400( c + v c \dfrac{c+v}{c} ), while f 1 f_1 =400( c c − v \dfrac{c}{c-v} ) where c is the speed of sound in still air. Obviously these two quantities are different. For the two apperant frequencies to be equal, the velocity of the moving observer with stationary source must be greater than the velocity of the moving source with stationary observer. If the velocities in the two cases be v1 and v2, then 1 v 1 \dfrac{1}{v1} - 1 v 2 \dfrac{1}{v2} = 1 c \dfrac{1}{c}

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