#### Question

A sonometer wire is in unison with a tuning fork of frequency 125 Hz when it is stretched by a weight. When the weight is completely immersed in water, 8 beats are heard per second. Find the specific gravity of the material of the weight.

#### Solution

Given:-

When wire is stretched by a weight hanging vertically, n_{1} = 125 Hz,

Let frequency of wire when the weight is immersed in water producing 8 beats per second = n_{2}

**∴** n_{2} = n_{1} - 8 = 125 - 8 = 117 Hz

To find: Specific gravity (ρ)

formula= `n_1/n_2=sqrt(rho/(rho-1))`

Calculation: From formula,

`125/117=sqrt(rho/(rho-1))`

`1.068=sqrt(rho/(rho-1))`

`therefore1.141=rho/(rho-1)`

`thereforerho=1.141(rho-1)`

`thereforerho=1.141rho-1.141`

`1.141=1.141rho-rho`

`thereforerho=1.141/0.141`

`thereforerho= antilog[log 1.141-log 0.141]`

`=antilog[0.0573-bar1 .1461]`

`=antilog[0.9112]`

`thereforerho=8.151`

**The specific gravity of material of the weight is 8.151.**