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

Answer

A

Explanation

From vibration mo `(lambda)/(2)=L rArr lambda = 2L`
`therefore` wave speed, `V=sqrt((Y)/(p)`
So, frequency `f = (v) /(lambda)`
`rArr f=(1)/(2L)sqrt((Y)/(p)) = = (1)/(2xx60xx10^(-2)) sqrt((9.27xx10^(10))/(2.7xx10^(3))approx 5000 Hz, f = 5 kHz`