Question

A sine wave is traveling in a medium. The minimum distance between the two particles, always having same speed, is

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

Answer 1

The correct option is C

$\frac{\lambda }{2}$

Explanation for the correct option:

1. When a sine wave passes through the string, the particles oscillate in simple harmonic motion.
2. At any point of time, the particles having equal displacement from the mean position will have equal speed and the minimum distance between these points will be $\raisebox{1ex}{$\lambda $}\!\left/ \!\raisebox{-1ex}{$2$}\right.$.
3. A sine wave has both maxima and minima and the particle displacement has a phase difference of $\mathrm{\pi }$ radians.
4. The speeds at the maximum point and the minimum point are the same although the direction of the motion is different. The difference between the positions of maxima and minima is equal to $\raisebox{1ex}{$\lambda $}\!\left/ \!\raisebox{-1ex}{$2$}\right.$.

Hence, option (C) is correct.