Two notes A and B sounded together produce 2 beats per second. When notes B and C are sounded together 3 beats with per second are produced. The notes A and C separately produce the same number of beats with a standard tuning fork of frequnecy 456 Hz. the possible frequency of 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):}`.