Question

A wave of angular frequency $\omega$ propagates so that a certain phase of oscillation moves along x-axis, y-axis and z-axis with speeds c${}_1,c_2$ and c${}_3$ respectively. The propagation constant $k$ is

• A. $\frac{\omega }{\sqrt{c_1^2+c_2^2+c_3^2}}(\hat{i}+\hat{j}+\hat{k})$
• B. $\frac{\omega }{c_1}\hat{i}+\frac{\omega }{c_2}\hat{j}+\frac{\omega }{c_3}\hat{k}$
• C. $(\omega \hat{i}+\omega \hat{j}+\omega \hat{k})\frac{1}{c}$
• D. $\frac{\omega }{(c_1+c_2+c_3)}(\hat{i}+\hat{j}+\hat{k})$

Answer 1

Answer: (B)

$\frac{\omega }{c_1}\hat{i}+\frac{\omega }{c_2}\hat{j}+\frac{\omega }{c_3}\hat{k}$

$K=\frac{w}{V}$
$K=\frac{w}{C_1}\hat{i}+\frac{w}{C_2}\hat{i}+\frac{w}{C_3}\hat{k}$