A tuning fork of frequency 100 when sounded together with another tuning fork of unknown frequency produces 2 beats per second. On loading the tuning fork whose frequency is not known and sounded together with a tuning fork of frequency 100 produces one beat, then the frequency of the other tuning fork is

Options

A. 102
B. 98
C. 99
D. 101

Answer

A

Explanation

Suppose nA is known frequency, then `n_(A) = 100 Hz, `and let `n_(B)` be the frequency of the other tuning fork
T = 2 =Beat frequency, which is decreasing after loading `(i.e. x darr)`
Unknown tuning fork is loaded so ngB decreases and also given that beat frequency is 1, so beat frequency also decreases
Hence, `n _(B) gt n _(A) and n _(B) - n _(A) = x `
`implies n _(B) = n _(A) + x = 100 + 2 = 102 Hz`