Question

In a standing wave on a string
A) In one time period all particles simultaneously at rest twice.
B) All the particles must be at their positive extremes simultaneously once in one time.
C) All the particles must be at their positive extremes simultaneously once in a time period.
D) All the particles are never at rest simultaneously.

Answer 1

Hint: Standing wave is a wave that does not move in space with time. Its peak amplitude remains constant with time. The standing wave occurs due to the interference between the two oppositely moving waves in a medium.

Complete step by step solution:
(i) When the two oppositely moving waves, which are in phase in one medium, the standing wave occurs there due to the interference between those two waves.
(ii) That standing wave has peak amplitude at any space that is constant with time. And the oscillations at any point in the wave are in phase with each other.
(iii) We can imagine the vibrational wave as a standing wave. The wave does not move, every particle comes at rest (zero) simultaneously and attains the peak value at the same time. The wave does this in a rhythmic motion.
(iv) Hence from the given options we cannot choose options B and C. As these points suggest that the particles reach their positive extremes in one time. But it does it in a rhythmic motion. And we cannot suggest the option D. Because it says that the particles are never at rest simultaneously.
(v) The important feature of the standing wave is that at one time, all the particles are at rest simultaneously. This point is suggested by option A.

Hence the correct option is A.

Note:
Standing waves are not moving in the medium; they just vibrate. The wave completely rests at one time. And it reaches its peak amplitudes in opposite directions at the same time. Hence the net energy of the standing waves will be zero. The standing waves are first noticed by Michael Faraday on the surface of the liquid in a vibrating container.