Question

What is the phase difference between two particles $25m$ apart in a wave represented by equation $y=0.03\sin (\pi [2t-0.01x])$ travelling in a medium?

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

Answer 1

Answer: (B)

Equation of wave is given as
$y=0.03\sin (\pi [2t-0.01x])$
Path difference, $\Delta x=25m$
Comparing the wave equation by
$y=A\sin (\omega t-kx)$, we get $k=0.01\pi$
$\Rightarrow \frac{2\pi }{\lambda }=0.01\pi$
$\Rightarrow \lambda =\frac{2}{0.01}$
$\Rightarrow \lambda =2\times 10^{2}m$
$\therefore$ Phase difference,
$\Delta \phi =\frac{2\pi }{\lambda }\times \Delta x$
$=\frac{2\pi }{2\times 10^2}\times 25$
$=\frac{\pi }{4}$