Question

A brass rod (density 8.3 g/cm³ ),3 m long is clamped at the centre, It is excited to give longitudinal vibrations and the frequency of the fundamental note is 600 Hz. Calculate the velocity of sound in the rod and its Young’s modulus.

Answer 1

Here, density of the brass rod

ρ= 8.3 g/cm³ = 8.3 x 10³ kg/m³

length of the rod, L = 3 m

frequency of the note produced, v = 600 Hz

Let the wavelength of vibration in the rod =λ 

As the rod is clamped at its centre, the centre is a node and free ends are antinodes.

Thus, λ = 2 L = 6m

If speed of sound in brass is v, then

or v = (600 Hz) (6 m) = 3.6 x 10³ m/s

Let Young’s modulus of the material of the rod = Y