Question

A wave equation which gives the displacement along the y-direction is given by $y=10\sin (60t+2x)$ where $x$ and $y$ are in metres and $t$ is time in seconds. This represents a wave

• A. travelling with a velocity of $30m/s$ in the negative $x-$direction
• B. of wavelength $\pi m$
• C. of frequency$\frac{30}{\pi }Hz$
• D. of amplitude $10m$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A travelling with a velocity of $30m/s$ in the negative $x-$direction
B of frequency$\frac{30}{\pi }Hz$
C of amplitude $10m$
D of wavelength $\pi m$

$v=\frac{dy}{dt}=10\times 60\times \cos (60t+2x)$
$velocity=\frac{w}{k}=\frac{60}{2}=30\frac{m}{s}$

As $y$ is of the form $A\sin (wt+kx)$, velocity is negative
$k=2,\lambda =\frac{2\pi }{k}=\pi m$
$f=\frac{w}{2\pi }=\frac{60}{2\pi }=\frac{30}{\pi }Hz$
Amplitude$=10m$
Thus a,b,c,d are correct answers.