Question

If the equation of motion of standing wave is $y=0.3\sin$ $(314t-1.57x),$ the velocity of standing wave is :

• A. 400 unit
• B. 250 unit
• C. 200 unit
• D. 150 unit

Answer 1

Answer: (C)

Key Idea: Standard equation of standing wave is $y=a\sin (\omega t=kx).$
When two identical transverse, progressive waves travel in a bounded medium with the same speed but in opposite directions then by their superposition a new type of wave is produced which appears stationary in the medium. This is called standing wave. Let a be the amplitude, $\omega$ angular velocity, k constant and $x$ displacement, then equation of standing wave is
$y=a\sin (\omega t-kx)$
Given, equation is
$y=0.3\sin (314t-1.57x)$
On comparing the two equations, we have
$\omega t=314t$ and $kx=1.57x$
$\Rightarrow$ $\omega =314$ and $k=1.57$
$\therefore$ velocity $v=\frac{\omega }{k}=\frac{314}{1.57}=200\text{unit}$