In a sonometer wire, the tension is maintained by suspending a 50.7 kg mass from the free end of the wire. The suspended mass has a volume of 0.0075 m 3. The fundamental frequency of the wire is 260 Hz . If the suspended mass is completely submerged in water, the fundamental frequency will become (take `g = 10 ms^(-2)`) [

Options

A. 220 Hz
B. 230 Hz
C. 240 Hz
D. 260 Hz

Answer

C

Explanation

`n_2/n_1 = sqrt(T_2/T_1)`
By archimedes principle `=T_1-T_2`
`=vrhog` = loss of weight in water
`therefore T_2=T_1-vrhog`
`n_2/n_1 = sqrt((T_1-vrhog)/(T_1))`
`=sqrt(((50.7-7.5xx10^(-3)xx10^3)g)/(50.7g))`
`=sqrt((43.2)/(50.7)) = sqrt(144/169)`
`n_2/n_1 = 12/13 therefore n_2 = 12/13 xx260 = 240Hz`