A train moves towards a stationary observer with speed 20 m/s. The train sounds a whistle and its frequency heard by the observer is f 1 . When the train moves away from the platform at a speed of 2

Question

A train moves towards a stationary observer with speed 20 m/s. The train sounds a whistle and its frequency heard by the observer is f 1 ​ . When the train moves away from the platform at a speed of 20 m/s, the frequency heard is f 2 ​ . If the speed of sound is 340 m/s, then f 1 ​ f 2 ​ ​ is

TestHub · Accepted Answer

Using Doppler's effect, the apparent frequency when the source moves towards a stationary observer is given by:

$f_{1} = f_{0} (\frac{v}{v - v _{s}})$

Substituting $v = 340$ m/s and $v_{s} = 20$ m/s:

$f_{1} = f_{0} (\frac{340}{340 - 20}) = f_{0} (\frac{340}{320})$

When the source moves away from the stationary observer, the apparent frequency is given by:

$f_{2} = f_{0} (\frac{v}{v + v _{s}})$

Substituting the values:

$f_{2} = f_{0} (\frac{340}{340 + 20}) = f_{0} (\frac{340}{360})$

Taking the ratio $\frac{f _{2}}{f _{1}}$ :

$\frac{f _{2}}{f _{1}} = \frac{f _{0} ( \frac{340}{360} )}{f _{0} ( \frac{340}{320} )} = \frac{320}{360} = \frac{8}{9}$

Answer: $\frac{8}{9}$

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