Question

The equation of a progressive wave is $y=0.5\sin 2\pi (\frac{t}{0.004}-\frac{x}{50})$, where $x$ is in $cm$. The phase difference between two points separated by a distance $5cm$ at any instant is :

• A. $\frac{\pi }{5}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{2}$
• D. $\pi$

Answer 1

The correct option is A $\frac{\pi }{5}$

$Wavelength\left(\lambda \right)=\frac{2\pi }{k}=\frac{2\pi \times 50}{2\pi }=50cm$

We know that path difference of $\lambda$ gives rise to phase difference of $2\pi$. So path difference of $5cm$ gives rise to phase difference of $\frac{2\pi }{\lambda }\times 5=\frac{\pi }{5}$