There is a set of four tuning forks , one with the lowest frequency vibrating at `550 Hz`. By using any two tuning forks at a time , the following beat frequencies are heard : `1 , 2, 3, 5 , 7 , 8`. The possible frequencies of the other three forks are

Options

A. `552 , 553 , 560`
B. `557, 558 , 560`
C. `552 , 553 ,558`
D. `551 , 553 , 558`

Answer

D

Explanation

As number of beats ` = Delta v`
For option (a), the frequencies are
`v_(1) = 550 Hz , v_(2) = 552 Hz , v_(3) = 553 Hz , v_(4) = 560 Hz`
The beats produced will be
`Delta v_(1) = v_(2) - v_(1) = 2`
`Delta v_(2) = v_(3) - v_(1) = 3`
`Delta v_(3) = v_(4) - v_(1) = 10`
`Delta v_(4) = v_(3) - v_(2) = 1`
`Delta v_(5) = v_(4) - v_(2) = 8`
`Delta v_(6) = v_(4) - v_(3) = 7`
which does not match with the given set of beat frequencies . Hence option (a) is not possible .
Similarly options (b) and (c ) are also not possible .
For options (d) , frequencies are `v_(1) = 550 , v_(2) = 551 , v_(3) = 553 , v_(4) = 558`
`Delta v_(1) = v_(2) - v_(1) = 1`
`Delta v_(2) = v_(3) - v_(1) = 3`
`Delta v_(3) = v_(4) - v_(1) = 8`
`Delta v_(4) = v_(3) - v_(2) = 2`
`Delta v_(5) = v_(4) - v_(2) = 7`
`Delta v_(5) = v_(4) - v_(2) = 7`
`Delta v_(6) = v_(4) - v_(3) = 5`
which matches with the given set of beat frequencies . Hence option (d).