Question

When a wave travels in a medium, the particle displacement is given by
$y(x,t)=0.03sin\pi (2t-0.01x)$
where y and x are expressed in metres and t in seconds. At a given instant of time, the phase difference between two particles 25 m apart is

• A. $\frac{\pi }{8}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{2}$
• D. $\pi$

Answer 1

The correct option is B

$\frac{\pi }{4}$

The particle displacement is given by
$y(x,t)=Asin\left\{\frac{2\pi }{\lambda }\right(vt-x\left)\right\}$
Comparing this with the given equation, we have
$\frac{2\pi }{\lambda }=0.01\pi$
$\Rightarrow \lambda =200m$
Now, phase difference, $\Delta \varphi =\frac{2\pi }{\lambda }\Delta x=\frac{2\pi }{200}\times 25=\frac{\pi }{4}$
Hence, the correct choice is (b).