Question

For a string clamped at both ends, which of the following wave equation is valid for a stationary wave set up in it whose origin is at one of the ends of the string?

• A. $y=A\sin kx\sin \omega t$
• B. $y=A\cos kx\sin \omega t$
• C. $y=A\cos kx\cos \omega t$
• D. $y=2A\cos kx\cos \omega t$

Answer 1

The correct option is A $y=A\sin kx\sin \omega t$


For the string clamped at both ends, the displacement of particle at these ends will always be zero.
So, both fixed ends will act as node,
i.e., $y=0$ at $x=0$ and $x=L$.
Therefore, only option $\left(a\right)$ satisfy the conditions for the stationary wave, $y=A\sin kx\sin \omega t$