One wave moves to the right and a second wave reflected) moves to the left to form a stationary wave. At which points) does the stationary wave have a node?
A) 1
B) 3 and 5
C) 2
D) 4 and 6
E) 2, 4, and 6

Question

One wave moves to the right and a second wave reflected) moves to the left to form a stationary wave. At which points) does the stationary wave have a node?
A) 1 
B) 3 and 5 
C) 2 
D) 4 and 6 
E) 2, 4, and 6

Quizplus · Accepted Answer

In a stationary wave, nodes are formed at points where the displacement is zero. 
At point 1, there is no reflected wave, so the displacement is the sum of the two waves which is non-zero. 
At points 2 and 6, the two waves are in phase and add up constructively, so the displacement is non-zero. 
At points 3 and 5, the two waves are out of phase and cancel each other out, so the displacement is zero and there is a node. 
At point 4, the two waves are in opposite directions, so the displacement is also zero and there is another node. Therefore, the stationary wave has nodes at points 3 and 5 as well as point 4, thus the best choice is D.

One Wave Moves to the Right and a Second Wave