A tuning fork A produces 4 beats with tuningfork B of frequency 256 Hz. When A is filed beats are found to occur at shorter intervals. What was its original frequency?

Explanation

As tuning fork Aproduces 4 beats with B of frequency `(f_B =256 Hz)`, the frequency of A, `f_A` will be `f_A = f_b pm 4 = 256 pm 4, i.e., f_A =252 Hz or 260 Hz`
Now on filing due to decrease in inertia frequency of A will increase and occurrence of beats at shorter duration means increase in beat frequency, so if `f_A= 252 Hz, 256 - f_A = 4Hz` and so with increase in `f_A` beat frequency will decrease. If `f_A =260 Hz, f_A -256 = 4 Hz` and so with increase in `f_A` beat frequency will increase and as on filing frequency increases.
`:.` The frequency of A before filing was 260 Hz