A source and listener are both moving towards each other with speed 10 V . (where V is speed of sound) If the frequency of sound note emitted by the source is ' n ', then the frequency hea

Question

A source and listener are both moving towards each other with speed 10 V ​ . (where V is speed of sound) If the frequency of sound note emitted by the source is ' n ', then the frequency heard by the listener would be nearly

TestHub · Accepted Answer

Using the Doppler effect formula for apparent frequency:

$n^{'} = n (\frac{V + V _{L}}{V - V _{S}})$

Since both the source and the listener are moving towards each other, the listener's velocity $V_{L}$ is taken as positive in the numerator and the source's velocity $V_{S}$ is taken as positive in the denominator.

Given $V_{L} = \frac{V}{10}$ and $V_{S} = \frac{V}{10}$ .

Substituting the values:

$n^{'} = n \frac{V + \frac{V}{10}}{V - \frac{V}{10}}$

$n^{'} = n \frac{\frac{11 V}{10}}{\frac{9 V}{10}}$

$n^{'} = n (\frac{11}{9})$

$n^{'} \approx 1.22 n$

Answer: 1.22 n

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