Question

A sinusoidal wave of frequency $500Hz$ has a speed of $350m/s$. The phase difference between two displacements at a certain point at times $1m$ apart is

• A. $\frac{\pi }{4}$
• B. $\frac{\pi }{2}$
• C. $\pi$
• D. $\frac{3\pi }{2}$

Answer 1

Answer: (C)

$v=350m/s$
$v=\frac{\omega }{k}$
$k=\frac{2\pi f}{v}$
$k=\frac{2\pi \times 500}{350}$
$k=\frac{2\pi }{0.7}$
$\therefore \lambda =0.7m$
Let equation of wave be
$y=A\sin (kx-\omega t)$
Let $x_1=0$
$x_2=1m$
$y_1=A\sin (\omega t)$
$y_2=A\sin \left(\frac{2\pi }{0.7}\times 1+\omega t\right)$
Hence phase difference $=\frac{20\pi }{7}$ or approximately
Phase difference $=3\pi$
Which is same as $\Delta \varphi =\pi$