Question

A wave in the string is defined by the function $y={\sin }^2\omega t$, then the time period of this function is

• A. $\frac{2\pi }{\omega }$
• B. $\frac{\pi }{\omega }$
• C. $\frac{\pi }{2\omega }$
• D. $\frac{4\pi }{\omega }$

Answer 1

The correct option is B $\frac{\pi }{\omega }$

We know that,
$y={\sin }^2\omega t=1-\cos 2\omega t$

Comparing above equation with general equation of sinusoidal wave, we can say:
$\Rightarrow 2\omega =\frac{2\pi }{T}$
$\Rightarrow T=\frac{\pi }{\omega }$