Question

The equation y = a sin^2(kx-wt) represent a wave motion? If yes, what is the amplitude and frequency

Answer 1

Answer:  The amplitude of the given wave equation is $\frac{a}{2}$.

The frequency of the given wave equation is represented by $\frac{\omega }{\pi }$.  

Explanation:

In the given problem,

The equation of the wave motion is given as follows;

y = a sin^2(kx-wt)  

Use the trigonometry formula.

$sin^{2}x=\frac{1}{2}(1-cos2x)$

Then the equation of the given wave becomes as;

$y=\frac{A}{2}(1-cos(2kx-2\omega x))$

The amplitude of the given wave equation is $\frac{a}{2}$.

The relation between angular frequency and frequency is as follows;

$\nu =\frac{\omega }{2\pi }$

According to modified given wave equation,

Put $\omega =2\omega$.

$\nu =\frac{\omega }{\pi }$

The frequency of the given wave equation is represented by $\frac{\omega }{\pi }$.  

Answer 2

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thnx for asking...