Question

A wave has a speed of $100\text{cm/s}$, and a frequency of $100\text{Hz}$. The phase difference between two points, $2.75\text{cm}$ apart, is,

• A. $0$ rad
• B. $\frac{11\pi }{2}$ rad
• C. $\frac{\pi }{4}$ rad
• D. $\frac{3\pi }{8}$ rad

Answer 1

The correct option is B $\frac{11\pi }{2}$ rad

Given:
$v=100\text{cm/s}=1\text{m/s}$
$f=100\text{Hz}$
$\Delta x=2.75\text{cm}$

The wavelength of the wave is given by,
$\lambda =\frac{v}{f}=\frac{1}{100}\text{m}=1\text{cm}$

The phase difference between the points is given by,
$\Delta \varphi =\frac{2\pi }{\lambda }\times \Delta x$
$\Delta \varphi =\frac{2\pi }{1}\times 2.75=5.5\pi \text{rad}=\frac{11\pi }{2}\text{rad}$

Hence, $\left(B\right)$ is the correct answer.