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 standard equation describing a sound wave is \( y = A \cos(kx - \omega t) \), where \( A \) represents the amplitude, \( k \) denotes the wave number, and \( \omega \) signifies the angular frequency. The velocity of the wave, \( v \), is determined by the equation: \[ v = \frac{\omega}{k}. \] Accordingly, the correct selection is option (1).