First slide

Doppler

Question

At each of two stations A and B, a siren is sounding with a constant frequency of 250 cycle $s^{- 1}$ . A cyclist from A proceeds straight towards B with a velocity of 12 km $h^{- 1}$ and hears 5 beats/s. The velocity of sound is nearly:

Moderate

A

328 ${ms}^{- 1}$
B

320 ${ms}^{- 1}$
C

333 ${ms}^{- 1}$
D

336 ${ms}^{- 1}$

Solution

If $f_{B}$ is the frequency as heard by cyclist from source B and $f_{A}$ is the frequency as heard by the cyclist from source A. Then $f_{B} - f_{A} = 5$
$250 (\frac{V_{s} + \frac{10}{3}}{V_{s}}) - 250 (\frac{V_{s} - \frac{10}{3}}{V_{s}}) = 5$
= 333 m/s

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