A piano string `1.5 m` long is made of steel of density `7.7 xx 10^(3) kg//m^(3) and gamma = 2 xx 10^(11) N//m^(2)`. It is maintained at a tension which produces an elastic strain of `1 %` in the string . What is the fundamental frequency of transverse vibration of the string ?

Options

A. 256 Hz
B. 178Hz
C. 170Hz
D. 200Hz.

Answer

B

Explanation

Note that `n=1/21sqrt(T/(pir^2d))` and `gamma =T/(pi r^2)` strain.
`therefore T/(pi r^2)=gamma ` x strain =`1/21sqrt((gamma xx "strain")/d)`