Question

A wave equation which gives the displacement of particle along $y-$ direction is represented as $y={10}^4\sin (60t+2x)$, where $x$ and $y$ are in $\text{metre}$ and $t$ in $\text{sec}$. Among the following choose the correct statement.

• A. It represents a wave propagating along positive $x-$ axis with a velocity of $30\text{m/s}$
• B. It represents a wave propagating along negative $x-$ axis with a velocity of $120\text{m/s}$
• C. It represents a wave propagating along negative $x-$ axis with a velocity of $30\text{m/s}$
• D. It represents a wave propagating along negative $x-$ axis with a velocity of ${10}^4\text{m/s}$

Answer 1

The correct option is C It represents a wave propagating along negative $x-$ axis with a velocity of $30\text{m/s}$

From the given wave function, $\omega =60,k=2$
Wave velocity is, $v=\frac{\omega }{k}=\frac{60}{2}=30\text{m/s}$
Since the displacement $\left(y\right)$ is of the form $A\sin (\omega t+kx)$, therefore wave velocity is along negative $x-$direction.
$\Rightarrow$Option $\left(c\right)$ is correct.