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 = 5n = 205Clearly n = 205 satisfies equation (2) .Now , if n is less than 200, then| n-200 | = -(n-200) = 5n = 195Clearly , n=195 does not satisfy equation (2).Therefore, n = 205 is the correct answer. Physics

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