Question

A string of length $L$ is stretched along the $x-axis$ and is rigidly clamped at its two ends. It undergoes transverse vibration. If $n$ is an integer, which of the following relations may represent the shape of the string at any time:-

• A. $y=A\sin \left(\frac{n\pi x}{L}\right)\cos \omega t$
• B. $y=A\sin \left(\frac{n\pi x}{L}\right)\sin \omega t$
• C. $y=A\cos \left(\frac{n\pi x}{L}\right)\cos \omega t$
• D. $y=A\cos \left(\frac{n\pi x}{L}\right)\sin \omega t$

Answer 1

Answer: (A), (B)

The correct options are
A $y=A\sin \left(\frac{n\pi x}{L}\right)\cos \omega t$
B $y=A\sin \left(\frac{n\pi x}{L}\right)\sin \omega t$