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Question

A source of frequency n gives $$5$$ beats per seconds when sounded with a source of frequency $$200$$ Hz. The second harmonic frequency $$2$$n of source gives $$10$$ beats/s. When sounded with a source of frequency $$420$$ Hz, the value of n is?


Solution

Beat frequency = |f - f'|
According to question , 
| n-200 | = 5                                                     ...(1)
and | 2n-420 | = 10                                          ...(2)
If n is greater than 200, then 
| n-200 | = n-200 = 5
n = 205
Clearly n = 205 satisfies equation (2) .
Now , if n is less than 200, then
| n-200 | = -(n-200) = 5
n = 195
Clearly , n=195 does not satisfy equation (2).
Therefore, n = 205 is the correct answer. 

Physics

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