Question

The equation of a simple harmonic wave is given by $y = 6\, Sin\, 2\pi(2t - 0.1x)$, where $x$ and $y$ are in $mm$ and $t$ is in seconds. The phase difference between two particles $2\, mm$ apart at any instant is

• A. 18$^\circ$
• B. 36$^\circ$
• C. 54$^\circ$
• D. $72^\circ$

Answer 1

Answer: (D)

From the given equation $k=0.2 \pi$
$\Rightarrow \,\,\,\, \frac{2 \pi}{\lambda} =0.2 \pi $
$\Rightarrow \,\,\, \lambda =10\, mm$
$\Delta \phi =\frac{2 \pi}{\lambda} \Delta x=\frac{2 \pi}{10} \times 2=\frac{2 \pi}{5}=72^{\circ}$