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 speed of the component progressive wave is:

• A. $120cm/sec$
• B. $20cm/sec$
• C. $40cm/sec$
• D. $6cm/sec$

Answer 1

The correct option is A $120cm/sec$

Given,
$y=6\sin \left(\frac{\pi x}{3}\right)\cos 40\pi t$
Comparing it with the standard form
i.e.
$y=2a\sin kx\cos \omega t$
$\omega =40\pi$
$k=\frac{\pi }{3}$
$\because k=\frac{2\pi }{\lambda }$
$\left(\frac{2\pi }{\lambda }\right)=\frac{\pi }{3}$
or $\lambda =6cm$
$\omega =40\pi$
$\because \omega =2\pi f$
$40\pi =2\pi f$
$f=20Hz$
$\because v=f\lambda$
$v=20\times 6$
$v=120cm/sec$

Final answer: (c)