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).