Question

For sine wave, the minimum distance between two particles which always have the same speed is:

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

Answer 1

The correct option is C $\frac{\lambda }{2}$

Let the sine wave have the form $y=A\sin (kx-\omega t)$

Thus the velocity of the wave has distribution $v=\frac{dy}{dt}=-A\omega \cos (kx-\omega t)$

We consider the wave at some instant of time, say $t=0$. Then the velocity of difference points is $-A\omega \cos \left(kx\right)$

Then the speed would be given by $A\omega |\cos \left(kx\right)|$

This function has a period $=\pi$

Thus $k{x}_2=\pi +k{x}_1$

$\Rightarrow k(x_2-x_1)=\pi$

$\Rightarrow x_2-x_1=\frac{\pi }{2\pi /\lambda }$

$=\frac{\lambda }{2}$.

Then the speed would be Option C is correct option.