Question

The equation of plane wave is given by as: $ y=2\,\sin \,\pi \left( 200\,t\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
$y=a \sin \frac{2 \pi}{\lambda}(v t-x)\,\,\,\,...(1)$

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