Question

If the equation of a standing wave is given by $y=6sin\pi xcos100\pi t$, the equation of the component waves are

• A. $y=3sin(\pi x+50\pi t)$ and $3sin(\pi x-50\pi t)$
• B. $y=3sin(\pi x+100\pi t)$ and $3sin(\pi x-100\pi t)$
• C. $y=6sin(\pi x+100\pi t)$ and $6sin(\pi x-100\pi t)$
• D. $y=6sin(\pi x+50\pi t)$ and $6sin(\pi x-50\pi t)$

Answer 1

The correct option is B $y=3sin(\pi x+100\pi t)$ and $3sin(\pi x-100\pi t)$

$y=6sin\pi xcos100\pi t$ can be written as $y=3sin(\pi x+100\pi t)-3sin(\pi x-100\pi t)=3sin(\pi x+100\pi t)+3sin(100\pi t-\pi x+\pi )$
Thus the component waves are $y=3sin(\pi x+100\pi t)$ and $3sin(100\pi t-\pi x)$ with a phase difference of $\pi$
The correct option is (b)