Question

An aluminium rod having a length $100$ cm is clamped at its middle point and set into longitude vibrations let the rod vibrate in its fundamental mode. The density of aluminium is $2600kg/m^3$ and its Young's modulus is $7.8\times {10}^{10}$$N/m^2$. the frequency of the sound produced is:

• A. $1250Hz$
• B. $2740Hz$
• C. $2350Hz$
• D. $1685Hz$

Answer 1

The correct option is B $2740Hz$

Given, $Length=100cm,density=2600kg/m^3$ Youngs modulus $=7.8\times {10}^{10}N/m^2$

The speed of the sound in the Aluminium will be:

$v=\sqrt{\frac{y}{\rho }}=\sqrt{\frac{7.8\times {10}^{10}}{2600}}=4800m/s$

The rod is clamped at the middle, the middle point is the pressure antinode. The ends of the rods are the nods. As the rods vibrates in its fundamental mode, there are no other nodes and antinodes. The length of the rod which also the distance between the successive nodes is equal to the half of the wavelength.

So, $l=2l=200cm=2m$

Thus, the frequency of the sound produced which is equal to the frequency of vibration of the rods is:

$n=\frac{v}{\lambda }=\frac{5480}{2}=2740Hz$