In a sonometer wire, the tension is maintained by suspending a `50 kg` mass from the free end of the wire. The suspended mass is completely submerged in water, the fundamental frequency will become …………… `Hz`.

Explanation

`c = v lamda` and `c = sqrt(T//m)`
`:. sqrt((T)/(m)) = v lamda`
where `T`= tension in the string and `m` = mass per unit length of wire
When `50.7 kg` mass is suspended for fundamental mode `lamda = 2l`
`v_(1) xx 2 l = sqrt((50.7 xx g)/(m))`
when mass in submerged in water, new tension
`T_(2)` = weight -upthrust
=`50.7 g - 0.0075 xx 1000 xx g = 43.3 g`
`:. v_(2) xx 2l = sqrt((43.3g)/(m))`
On dividing Eqs. (i) and (ii), we get
`(v_(2))/(v_(1)) = sqrt((43.2)/(50.7)) rArr v_(2) = v_(1) sqrt((43.2)/(50.7))`
=`260 sqrt((43.2)/(50.7)) = 240 Hz`.