Question

In a sound wave, the displacement of the air particles follows the equation $y = A \cos(kx - \omega t)$. What is the wave velocity?

• A. $v = \frac{\omega}{k}$
• B. $v = \frac{k}{\omega}$
• C. $v = \frac{A}{k}$
• D. $v = \frac{\omega}{A}$

Hint:

For a wave, the velocity is related to the angular frequency $\omega$ and the wave number $k$ by $v = \frac{\omega}{k}$.

Answer 1

The Correct Option is A

The general wave equation for a sound wave is $y = A \cos(kx - \omega t)$, where:

• $A$ is the amplitude,
• $k$ is the wave number,
• $\omega$ is the angular frequency.

The wave velocity $v$ is given by the formula: $$v = \frac{\omega}{k}.$$ Thus, the correct answer is option (1).