First slide

Doppler's effect

Question

A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered by the observer is f₁. If the train’s speed is reduced to 17 m/s, the frequency registered is f₂. If the speed of sound is 340 m/s then the ratio $f_{1} / f_{2}$ is

Moderate

A

18/19
B

1/2
C

2
D

19/18

Solution

By using $n' = n (\frac{v}{v - v_{S}})$
$\Rightarrow f_{1} = n (\frac{v}{v - v_{S}}) = n (\frac{340}{340 - 34}) = \frac{340}{306} n$
and $f_{2} = n (\frac{340}{340 - 17}) = n (\frac{340}{323}) \Rightarrow \frac{f_{1}}{f_{2}} = \frac{323}{306} = \frac{19}{18}$

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