Question

In a stationary wave represented by y = $a\sin \left(\omega t\right)\cos \left(kx\right)$ amplitude of the component progressive wave is

• A. $\frac{a}{2}$
• B. a
• C. 2a
• D. None of these

Answer 1

The correct option is A $\frac{a}{2}$

$y=a\sin \left(\omega t\right)\cos \left(kx\right)$.

$=\frac{a}{2}\left[2\sin \left(wt\right)\cos kx\right]$

As e know

$2\sin A\cos B=\sin (A+B)+\sin (A-B)$

$\therefore$ y can be written as

$y=\frac{a}{2}\left[\sin (wt+kx)+\sin (wt-kx)\right]y=\frac{a}{2}\sin (wt+kx)+\frac{a}{2}\sin (wt-kx)$

Component wave $1$

$y_1=\frac{a}{2}\sin (wt+kx)$

Here amplitude $=\frac{a}{2}$

Component wave $2$

$y_2=\frac{a}{2}\sin (wt-kx)$

Here amplitude $=\frac{a}{2}$

Hence option (A) is correct.