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Question

Two aeroplanes are travelling along parallel lines with the same velocity. The person in one aeroplane is hearing the  sound of another aeroplane. If the ratio of actual frequency and apparent frequency of sound when two aeroplanes are approaching to each other is $$4:5$$, the ratio of actual frequency and apparent frequency of same sound when same two aeroplanes are moving away from each other is:


A
5:6
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B
6:7
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C
5:9
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D
5:4
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Solution

The correct option is D $$5:4$$
Suppose both the planes has a velocity $$V_s$$. 
Now when they are approaching each other then the change of frequency will be: $$n_1=n\dfrac{V+V_s}{V-V_s}$$
Now, when they are moving away from each other then the change of frequency will be: $$n_2=n\dfrac{V-V_s}{V+V_s}$$ 
We can see that: $$\dfrac{n}{n_2}=\dfrac{n_1}{n}$$ 
So here, the ratio of actual frequency and apparent frequency of same sound when same two aeroplanes are moving away from each other is $$5:4$$

Physics

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