Question

For a travelling wave represented by equation,
$y=0.1\sin \pi (x-330t+\frac{2}{3})$ (SI units)
The phase difference between particles at $x_1=3\text{m}$ and $x_2=3.5\text{m}$ is

• A. $\frac{\pi }{2}$
• B. $\pi$
• C. $\frac{3\pi }{2}$
• D. $2\pi$

Answer 1

The correct option is A $\frac{\pi }{2}$

Given,
$y=0.1\sin \pi (x-330t+\frac{2}{3})$
Let $x_1=3\text{m}$ and $x_2=3.5\text{m}$ be two points on the wave.
The difference in distance between these points is,
$\Delta x=x_2-x_1=(3.5-3)=0.5\text{m}$
Now keeping the time constant;
From the wave equation, the phase at position $x_2$ is,
${\varphi }_2=\pi (x_2-330t+\frac{2}{3})$

Keeping the time constant;
The phase at position $x_1$ is,
${\varphi }_1=\pi (x_1-330t+\frac{2}{3})$
Hence phase difference is:
$\Rightarrow \Delta \varphi ={\varphi }_2-{\varphi }_1=\pi (x_2-x_1)$
$\Rightarrow \Delta \varphi =\pi \times 0.5$
$\therefore \Delta \varphi =\frac{\pi }{2}$