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?

Answer 1

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.