Question

The speed of a stationary wave represented by the equation $y = 0.75 \sin\left(\dfrac{7\pi}{4}x\right)\cos(350\pi t)$ is

• A. $100~\text{m/s}$
• B. $150~\text{m/s}$
• C. $160~\text{m/s}$
• D. $200~\text{m/s}$

Hint:

In a stationary wave, use $v = \omega / k$ to find wave speed from the wave equation.

Answer 1

The Correct Option is D

Given wave equation: $y = A \sin(kx) \cos(\omega t)$
Here, $k = \dfrac{7\pi}{4}$ and $\omega = 350\pi$
Wave speed $v = \dfrac{\omega}{k} = \dfrac{350\pi}{\dfrac{7\pi}{4}} = 350\pi \cdot \dfrac{4}{7\pi} = 200~\text{m/s}$