devarshi-dt-logo

Question:

A granite rod of 60cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7×10³ kg/m³ and its Young's modulus is 9.27×10¹⁰ Pa. What will be the fundamental frequency of the longitudinal vibrations?

5kHz

2.5kHz

10kHz

7.5kHz

Solution:

Given : Y = 9.27×10¹⁰ Pa, ρ = 2.7×10³ kg/m³, Length of rod L = 60 cm = 0.6 m
Velocity of sound in granite v = √(Y/ρ) = √(9.27×10¹⁰ / 2.7×10³) = 5.9×10³ m/s
Fundamental frequency ν = v/2L = (5.9×10³)/(2×0.6) = 5 kHz