Figure, shows a stationary wave between two fixed points P and Q. Which point(s) of 1, 2 and 3 are in phase with the point X?

A. 1, 2 and 3
B. 1 and 2 only
C. 2 and 3 only
D. 3 only

Hint: Remind the conditions for the two points on a stationary wave to be in phase. Use the condition for the position as well as direction of motion of the points with respect to each other.

Complete step by step answer:
A stationary wave between two fixed points P and Q with points X, 1, 2 and 3 is as below:

The two points on the stationary wave are in the same phase if they are at the same magnitude of distance from the equilibrium and if they have the same direction of motion or displacement.

The points X, a, 2 and 3 are at the same distance from the equilibrium position as they all are at the equilibrium position.

The point 1 on the stationary wave has the direction of displacement exactly opposite to that of point X. Hence, it is not in phase with the point X.

The point 2 on the stationary wave also has the direction of displacement exactly opposite to that of point X. Hence, point 2 is also not in phase with point X.

The point 3 on the stationary wave also has the direction of displacement exactly the same as that of point X. Hence, point 3 is in phase with point X.

Therefore, out of points 1, 2 and 3, point 3 is only in phase with the point X.

So, the correct answer is “Option D”.

Note:
The directions of displacement of points 1 and 2 are opposite as compared to point X because if the point X moves in the upper direction, the points 1 and 2 move in the lower direction and vice versa.