Question

A steel rod of length $100cm$ is clamped at the middle. The frequency of the fundamental mode for the lognitudinal vibrations of the rod is
(Speed of sound is steel $=5km{s}^{-1}$)

• A. $1.5kHz$
• B. $2kHz$
• C. $2.5kHz$
• D. $3kHz$

Answer 1

Answer: (C)

$2.5kHz$

Here,

$L=100cm=1m$,

$\nu =5km{s}^{-1}=5\times {10}^{3}m{s}^{-1}$

As the clamped at the middle, therefore the middle point is a node. In the fundamental mode, the antinode is formed at each end as shown in figure.

Therefore, the distance two consecutive aninodes is $\frac{\lambda }{2}$.

$\therefore \frac{\lambda }{2}=1m$ or $\lambda =2m$

The frequency of the fundamental mode is

$\upsilon =\frac{\nu }{\lambda }=\frac{5\times {10}^{4}m{s}^{-1}}{2m}=2.5\times {10}^{3}Hz=2.5kHz$