A sonometer wire is in unison with a tuning fork of frequency 150 Hz. If the tension in the wire is increased by 1%, how many beats per second will be heard ?

Explanation

Given, `v_(1) = 150` Hz
Let initial tension in the wire be `T_(1)` = 100 units
If it is increased by 1%, then new tension `T_(2)` = 101 units
Now, `(v_(2))/(v_(1)) = sqrt((T_(2))/(T_(1))) = sqrt((101)/(100)) = (1 + (1)/(100))^(1/2)`
`~~ 1 + (1)/(2) xx (1)/(100) = 1.005`
`v_(2) = 1.005 v_(1) = 1.005 xx 150 = 150.75` Hz
Beat frequency `= v_(2) - v_(1) = 150.75 - 150`
= 0.75 Hz