Question

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

• A. amplitude $A$ , frequency $\frac{\omega }{2\pi }$
• B. amplitude $\frac{A}{2}$, frequency $\omega /\pi$
• C. amplitude $2A$, frequency $\frac{\omega }{4\pi }$
• D. Does not represent a wave motion

Answer 1

The correct option is B amplitude $\frac{A}{2}$, frequency $\omega /\pi$

In the given problem,

The equation of the wave motion is given as follows;

y = a sin²(kx-wt)

Use the trigonometry formula.

sin²x = 1/2 ( 1- cos2x )

Then the equation of the given wave becomes as;

y = A/2 ( 1- cos(2kx - 2wx) )

The amplitude of the given wave equation is . A/2

The relation between angular frequency and frequency is as follows;

v = w/2π

According to modified given wave equation,

Put . w = 2π

v = w/π

The frequency of the given wave equation is represented by . w/π