Question

The equation $y=Asi{n}^2(kx-\omega t)$ represents a wave with

• A. amplitude A frequency $\omega /2\pi$
• B. amplitude A /2 frequency $\omega /\pi$
• C. amplitude 2A frequency $\omega /4\pi$
• D. It does not represent a wave motion

Answer 1

The correct option is B amplitude A /2 frequency $\omega /\pi$

$y=A{\sin }^2(kx-\omega t)=\frac{A}{2}\{1-\cos (2kx-2\omega t\left)\right\}$
Comparing the above equation with standard progressive wave equation
$y=A\sin (kx-\omega t)$, we get

Frequency ${\nu }^{\prime }=\frac{{\omega }^{\prime }}{2\pi }=\frac{2\omega }{2\pi }=\frac{\omega }{\pi }$ and amplitude $A^{\prime }=A/2$
Ans: B