First slide

Doppler's effect

Question

A whistle sends out 256 waves in a second. If the whistle approaches the observer with velocity 1/3 of the velocity of sound in air, the number of waves per second the observer will receive

Moderate

A

384
B

192
C

300
D

200

Solution

Wave number = $\frac{1}{λ}$ but $\frac{1}{λ'} = \frac{1}{λ} (\frac{v}{v - v_{s}}) and v_{s} = \frac{v}{3}$
$∴$ (W.N.)’ = (W.N.) $(\frac{v}{v - v / 3}) = 256 \times \frac{v}{2 v / 3}$
$= \frac{3}{2} \times 256 = 384$

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