Question

A progressive wave is, y = 12 sin (5t-4x), where all the quantities are in SI units. On this wave, how far away are the two points having a phase difference of $\pi/2$

• A. $\pi/4$
• B. $\pi/8$
• C. $\pi/16$
• D. $\pi/32$

Answer 1

Answer: (B)

$\pi/8$

Answer 2

The phase of the wave is

$$\phi = 5t - 4x.$$

For a fixed time (say $t=t_0$), the phase difference between two points $x_1$ and $x_2$ is

$$\Delta \phi = 4|x_2 - x_1| = \frac{\pi}{2}.$$

Thus,

$$|x_2 - x_1| = \frac{\pi/2}{4} = \frac{\pi}{8}.$$

The two points are separated by $\displaystyle \frac{\pi}{8}$.