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A fork sounded with frequency of 510Hz gives 8 beats per second and when tuned with another tuning fork of ν = 524Hz produces 6 beats. Find the frequency of the source

A fork sounded with frequency of 510Hz gives 8 beats per second and when tuned with another tuning fork of ν = 524Hz produces 6 beats. Find the frequency of the source Correct Answer 518Hz

CONCEPT: 

  • Beats are produced due to the interference of two waves which are slightly different in frequencies or one rise or fall in frequencies can be termed as beats

⇒ Beat frequency  = Number of betas per second  = Difference in frequencies between sources.

  • The unknown frequency of the source can be found out using the formula

⇒ Unknown frequency  = Known frequency ± beat frequency

CALCULATION : 

Given - ν = 510Hz, b = beats of the first source = 8 , ν1 = 524Hz and b1 = 6 beats

The unknown frequency of the tuning fork can be written in two equations given as

⇒ unknown frequency = ν ± b = 510 ± 8 = 518Hz or 502 Hz        ------(1)

⇒ unknown frequency = ν1 ± b1 = 524 ± 6 = 530Hzor 518 Hz      ------(2)

Comparing the equation 1 and 2  the common frequency is 518Hz

  • Hence option 2 is the answer

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