Question

The equation of plane wave is given by as: $y=2\sin \pi \left(200t\frac{x}{150}\right)$ When displacement $y$ is given in cms and time $t$ in second, then the velocity of the wave is:

• A. 30000 cm/s
• B. 200 cm/s
• C. 150 cm/s
• D. 2 cm/s

Answer 1

Answer: (A)

Compare the given equation with standard one.
The standard equation of a plane progressive wave is
$y=a\sin \frac{2\pi }{\lambda }(vt-x)...(1)$

where $\lambda$ is wavelength, $v$ is velocity, $t$ is time and $a$ is amplitude.
Given equation is
$y=2\sin \pi \left(200t-\frac{x}{150}\right)...(2)$
Comparing Eqs. (1) and (2)
$\frac{2\pi }{\lambda }=\frac{\pi }{150}$
$\Rightarrow \lambda =300cm$
and $\frac{2\pi }{T}=200\pi$
$\Rightarrow T=\frac{1}{100}s$
Frequency $(n)=\frac{1}{T}=\frac{1}{1/100}=100Hz$
Also velocity $=$ frequency $\times$ wavelength
$=100\times 300$
$-30000cm/c$