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Frequency of vibrations of a clamped metal rod

Physics Asked by Chaitanya Garg on March 14, 2021

On what factors will the frequency of vibration of a metal rod depend? Is it necessary that the rod will vibrate in fundamental mode when is clamped at its ends or it can vibrate at any frequency?

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2 Answers

It's not necessary that the rod will vibrate with fundamental frequency but with any frequency satisfying the boundary condition so that $$e^{ikx}=e^{ik(x+l/2)}$$ $$Rightarrow k=frac{pi n}{l}Rightarrow boxed{lambda=frac{l}{2n}}$$ where $n$ is an integer.

Answered by Young Kindaichi on March 14, 2021

You have represented a standing wave in the figure. A standing wave is created by superposition of traveling waves. The frequency of traveling waves will depend on the frequency of applied/driving force. To change the mode of vibration you can change the frequency of the driving force or change the tension in the rod.

You can observe it in this video. https://m.youtube.com/watch?v=-k2TuJfNQ9s

Answered by Naman Parikh on March 14, 2021

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