Question

The equation of a wave is $y=5\sin (\frac{t}{0.04}-\frac{x}{4})$; where $x$ is in $cm$ and $t$ is in second. The wave velocity of the wave will be

• A. $2.5{ms}^{-1}$
• B. $2{ms}^{-1}$
• C. $1.5{ms}^{-1}$
• D. $1{ms}^{-1}$

Answer 1

The correct option is D $1{ms}^{-1}$

For the wave, $y=A\sin (\omega t-kx)$, wave velocity is constant and is given by $\frac{\omega }{k}$.

On comparing the given wave with the above form of wave equation,

we find $\omega =\frac{1}{0.04}=25rad/s$ and $k=0.25c{m}^{-1}=25m^{-1}$.

Thus, in the given scenario, wave velocity is $\frac{\omega }{k}=\frac{25}{25}=1m/s$