A sonometer wire of length `1.5m` is made of steel. The tension in it produces an elastic strain of `1%`. What is the fundamental frequency of steel if density and elasticity of steel are `7.7 xxx 10^(3) kg//m^(3)` and `2.2 xx 10^(11) N//m^(2)` respectively ?

Options

A. (a) `188.5 Hz`
B. (b) `178.2 Hz`
C. ( c ) `200.5 Hz`
D. (d) `770 Hz`

Answer

B

Explanation

(b) Fundamental frequency,
`f = (v)/(2l) = (1)/(2l)sqrt((T)/(mu)) = (1)/(2l)sqrt((T)/(Arho))[`because` `v = sqrt((T)/(mu))` and `mu = (m)/(l)]`
Also,`Y = (Tl)/(ADeltal)` rArr `(T)/(A) = (YDeltal)/(l)` rArr `f = (1)/(2l)sqrt((gammaDeltal)/(lrho))` ........(i)
Putting the value of `l`, `(Deltal)/(l)`, `rho` and `gamma` i n `eq^(n)`. (i)we get,
`f = sqrt((2)/(7)) xx (10^(3))/(3)` or, `f~~ 178.2 Hz`