A metallic wire with tension T and at temperature `30 ^0 C` vibrates with its fundamental frequency of 1 kHz. The same wire with the same tension but at `10 ^0 C` temperature vibrates with a fundamental frequency of 1.001 kHz. The coefficient of linear expansion of the wire is

Options

A. `2xx10^-4//""^(@)C`
B. `1.5xx10^-4//""^(@)C`
C. `1xx10^-4//""^(@)C`
D. `0.5xx10^-4//""^(@)C`

Answer

D

Explanation

frequency of a wire `n=1/2lsqrt(T/m)`
`n prop1/l`
`n_1/n_2=l_2/l_1`
`1/1.001=l_2/l_1`
`/_\t=30-10=20^0C`
`implies l_2/l_1=(1-alpha/_\t)`
`1/1.001=(1-alphaxx20)`
`20alpha=1-1/1.001=0.001/1.001`
`:. alpha= 1/(1001xx20)=0.5xx10^-4//C`