A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is `2.7 xx10^(3) kg//m^(3)` and its Young’s modulus is `9.27 xx10^(10)` Pa. What will be the fundamental frequency of the longitudinal vibrations ?

Options

A. 10 kHz
B. 7.5 kHz
C. 5 kHz
D. 2.5 kHz

Answer

C

Explanation

There will be node at the centre and anti-node at both the ends hence fundamental frequency can be written as follows :
`f_(0) = (v)/(2l) = (1)/(2l) sqrt((Y)/(rho))`
`rArr" "f_(0) = (1)/(2(0.6)) sqrt((9.27 xx 10^(10))/(2.7 xx 10^(3)))`
`= 4.9 xx 10^(3) Hz ~~ 5` kHz.
Hence option (c) is correct.