A tunnig fork of frequency 256 Hz produces 4 beats per second with a wire of length 25 cm vibrating in its fundamental mode. The beat frequency decreases when the length is slightly shortened. What could be the minimum length by which the wire be shortened so that it produces no beats with the tuning fork ?

Answer

039 cm

Explanation

On decreasing length of wire its frequency increasest hus frequency of wire initialy was 252Hz
Thus we use `252 = (1)/(2(0.25))sqrt((T)/(mu))`
On changing wire length to l' its frequency becomes 256 Hz and beats becomes zero
`256 =(1)/(2(l') )sqrt((T)/(mu))`
`(l')/(0.25) = (252)/(256)`
l' = 0.24m
0.25 - 0.246 = 0.0039m = 0.39 cm.