The equation y=A ^2(kx- ) represents a wave motion with: - Vidyadip

MCQ

The equation $\text{y}=\text{A}\sin^2(\text{kx}-\omega\text{t})$ represents a wave motion with:

A
Amplitude A, frequency $\frac{\omega}{2\pi}$
✓
Amplitude $\frac{\text{A}}{2},$ frequency $\frac{\omega}{\pi}$
C
Amplitude 2A, frequency $\frac{\omega}{4\pi}$
D
Does not represent a wave motion.

✓

Answer

Correct option: B.

Amplitude $\frac{\text{A}}{2},$ frequency $\frac{\omega}{\pi}$

Explanation:
$\text{y}=\text{A}\sin^2(\text{kx}-\omega\text{t})$
$\Big[\cos^2\theta=1-2\sin^2\theta,\ \sin^2\theta=\frac{1-\cos^2\theta}{2}\Big]$
$\text{y}=\text{A}\Big[\frac{1-\cos^2(\text{kx}-\omega\text{t})}{2}\Big]$
$\text{y}=\frac{\text{A}}{2}\Big[1-\cos^2(\text{kx}-\omega\text{t})\Big]$
Thus, we have:
Amplitude $=\frac{\text{A}}{2}$
Frequency $=2\Big(\frac{\omega}{2\pi}\Big)$
$=\frac{\omega}{\pi}$

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