A tuning fork of frequency `256 H_(Z)` produces `4` beats per second with a wire of legth `25 cm` vibrating in its fundamental mode. The beat frequency decrease 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?

Explanation

`f prop (1)/(l)`
By decreasing the length, frequency of wire will
increase. But beat frequency is decreasing. Hence,
its original frequency was `(256 - 4) H_(Z)` or `252 H_(Z)` .
Now, we have to make it `256 H_(Z)` for no beats.
`(f_(1))/(f_(2)) = (l_(2))/(l_(1))`
`:. l_(2) = ((f_(1))/(f_(2))) l_(1)`
`= ((252)/(256))(25)`
`= 24.6 cm`
`:. Deltal = l_(2) - l_(2) = 0.4 cm`