Question

What is the phase difference between two particles $25\, m$ apart in a wave represented by equation $y=0.03 \sin (\pi[2 t-0.01\, x])$ 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
$y=0.03 \sin (\pi[2 t-0.01\, x])$
Path difference, $\Delta x=25\, m$
Comparing the wave equation by
$y=A \sin (\omega t-k x)$, 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,
$\Delta \varphi=\frac{2 \pi}{\lambda} \times \Delta x$
$=\frac{2 \pi}{2 \times 10^{2}} \times 25$
$=\frac{\pi}{4}$