Two notes `A` and `B`, sounded together, produce `2` beats per sec. Notes `B` and `C` sounded together produce `4` beats per sec. The notes `A` and `C` separately produce the same number of beats with a standard tuning fork of `456 Hz`. The possible frequency of the note `B` is

Options

A. `453.5 Hz`
B. `455.5 Hz`
C. `456.5 Hz`
D. `458.5 Hz`

Answer

A, B, C, D

Explanation

Let frequency of note `B` be `n` then according to question
`{:(n_(A)=n-2or n+2),(n_(C)=n-3 or n+3):}`
As `A` & `C` produce same number of beats with `T.F` of frequency `456 Hz` so
`{:((n-2)-456=456-(n-3)rArr n=458.5 Hz),((n+3)-456=456-(n-2)rArr n=455.5 Hz),((n+2)-456=456-(n-3)rArr n=456.5 Hz),((n+3)-456=456-(n+2)rArr n=453.5 Hz):}`.