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 frequency of the component progressive wave is :

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

Answer 1

The correct option is C $20Hz$

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

Final answer: (a)