Question

A metal rod 40cm long is dropped on to a wooden floor and rebounds into air. Compressional waves of many frequencies are thereby set up in the rod. If the speed of compressional waves in the rod in 5500 m/s, what is the lowest frequency of compressional waves to which the rod resonated as it rebounds?

• A. 675 Hz
• B. 6875 Hz
• C. 16875 Hz
• D. 0 Hz

Answer 1

Answer: (B)

6875 Hz

Both ends of the bar will be free so antinodes will exist there.In the lowest resonance form(i.e. the one with the longest segments), only one node will exist on the bar, at its center.

We will have

$L=2\left(\frac{\pi }{4}\right)=\frac{\pi }{2}$

$\lambda =2L=2\left(0.4\right)=0.8m$

$f=\frac{v}{\lambda }=\frac{5500}{0.8}=6875Hz$

It is the lowest frequency of compressional wave to which the rod resonated.