# If V is the velocity of the wave and $\omega$ is the angular velocity, then the propagation constant (K) of the wave is given by Option 1) $K=\frac{V}{\omega}$ Option 2) $K=\frac{\omega}{V}$ Option 3) $K=\frac{2\omega}{V}$ Option 4) $K=\frac{2V}{\omega}$

As we learnt in

Speed of sinusoidal wave -

Wave Speed

$\tfrac{dx}{dt}= V=\frac{\omega }{k}$

- wherein

$\omega = 2\pi \nu$

$K= \frac{2\pi }{\lambda }$

Relation between V & K is

$V=\nu\lambda=\:(\frac{\omega }{2\pi}).(\frac{2\pi}{K})=\frac{\omega}{K}$

or $K=\frac{\omega}{V}$

Option 1)

$K=\frac{V}{\omega}$

This option is incorrect.

Option 2)

$K=\frac{\omega}{V}$

This option is correct.

Option 3)

$K=\frac{2\omega}{V}$

This option is incorrect.

Option 4)

$K=\frac{2V}{\omega}$

This option is incorrect.

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