Question

A simple harmonic progressive wave is represented as $y = 0.03 \,sin \,\pi(2t - 0.01x)\, m$ . At a given instant of time, the phase difference between two particles $25\, m$ apart is

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

Answer 1

Answer: (C)

The given equation of SHM wave is
$y =0.03 \sin \pi(2 t-0.01 x) m $
$=0.03 \sin (2 \pi t-0.01 \pi x) m$
Compairing it with general equation, we get
$y=a \sin (\omega t-k x)$
where,$\,\,\,\,\,k=\frac{2 \pi}{\lambda} \Rightarrow \lambda=200 \,m$
The phase difference between two particles is
given by $\,\,\,\,\Delta \phi=k x=\frac{2 \pi}{\lambda} \times x \,\,\,\,\,\,...(i)$
Here, $\,\,\,\,x=25 \,m$
Substituting the values of $x$ and $\lambda$ in Eq. (i), we get
$\Delta \phi=\frac{2 \pi}{200} \times 25=\frac{\pi}{4} rad$