Question

A travelling harmonic wave is represented by the equation $y(x,t)={10}^3\sin (50t+2x),$ where $x$ and $y$ are in meter and $t$ is in seconds. Which of the following is a correct statement about the wave?

• A. The wave is propagating along the positive x - axis with speed $25{\text{ms}}^{-1}$
• B. The wave is propagating along the positive x - axis with speed $100{\text{ms}}^{-1}$
• C. The wave is propagating along the negative x - axis with speed $100{\text{ms}}^{-1}$
• D. The wave is propagating along the negative x - axis with speed $25{\text{ms}}^{-1}$.

Answer 1

The correct option is D The wave is propagating along the negative x - axis with speed $25{\text{ms}}^{-1}$.

Comparing the given equation i.e.

$y={10}^{-3}\sin (50t+2x)$ with standard equation,

$y=a\sin (\omega t-kx)$

$\Rightarrow$ Wave is travelling along $-vex-$ axis with speed $v=\frac{\omega }{k}\Rightarrow v=\frac{50}{2}=25{\text{ms}}^{-1}$