Question

The equation of a stationary wave is given by $y=6\sin \left(\frac{\pi x}{3}\right)\cos 40\pi t$ where $y$ and $x$ are given in $cm$ and time $t$ in second. Then the time period of the component progressive wave is :

• A. $\left(\frac{1}{20}\right)sec$
• B. $20sec$
• C. $40sec$
• D. $\left(\frac{1}{10}\right)sec$

Answer 1

The correct option is A $\left(\frac{1}{20}\right)sec$

Given,
$y=6\sin \left(\frac{\pi x}{3}\right)\cos 40\pi t$
Comparing it with the standard form i.e.
$y=2a\sin kx\cos \omega t$
$\omega =40\pi$
$\because \omega =\frac{2\pi }{T}$
$\left(\frac{2\pi }{T}\right)=40\pi$
$\Rightarrow T=\left(\frac{1}{20}\right)sec$

Final answer: (c)