Physics

Problem

A student writes the relation

v=\dfrac{k}{\omega}

for the speed

v

of a progressive wave. Check whether the relation is dimensionally correct. If not, write the correct relation involving

v

k

and

\omega

Intuitive explanation

The key to dimensional analysis is checking whether both sides of an equation have the same units. Here, $k$ (wavenumber) has dimensions of inverse length, while $\omega$ (angular frequency) has dimensions of inverse time—so their ratio gives inverse length per inverse time, which is velocity. The student's relation is actually dimensionally correct, but it's missing the physical insight: the speed of a wave depends on the product of wavelength and frequency, not their ratio. The correct relation is $v = \frac{\omega}{k}$ , which properly connects wave properties to propagation speed.

Intuitive explanation

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