Question

A wave travelling along a string is described by $y(x,t)=A\sin (kx-\omega t)$ in which the numerical constants are in SI units. Then which of the following statements is true?

• A. The acceleration of the wave can be given by $a(x,t)={\omega }^{2}y(x,t)$
• B. The acceleration of the wave can be given by $a(x,t)=-\omega y(x,t)$
• C. The acceleration of the wave can be given by $a(x,t)=-{\omega }^{2}y(x,t)$
• D. The acceleration of the wave can be given by $a(x,t)=\omega y(x,t)$

Answer 1

The correct option is C The acceleration of the wave can be given by $a(x,t)=-{\omega }^{2}y(x,t)$

We know that, the displacement of a transverse wave is given by $y=A\sin (kx-\omega t)$

Thus, the velocity is given by $v=\frac{dy}{dt}=A\omega \cos (kx-\omega t)$

Thus, the particle acceleration is given by $a=\frac{d^{2}y}{d{t}^2}=-A{\omega }^2\sin (kx-\omega t)$

Thus, at any instant, the particle acceleration is given by $a=-{\omega }^{2}y$