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The equation of a plane progressive wave is given by \( \boldsymbol{y}=\boldsymbol{A} \sin (\boldsymbol{\omega} \boldsymbol{t}-\boldsymbol{k} \boldsymbol{x}) \) The dimension of \( (\omega / k) \) is that of

1. frequency
2. velocity
3. wavelength
4. inverse of velocity

Correct answer: velocity

Solution

In a wave equation, the quantity inside the sine must be dimensionless, so ω has units of s⁻¹ and k has units of m⁻¹. Therefore ω/k has units of m s⁻¹, which is velocity.

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