The figure shows a wave on a string approaching its fixed end at a wall. When the wave reaches the wall and is reflected, a standing wave is set up in the string. One will observe a node at position
A) 1.
B) 2.
C) 3.
D) 4.
E) 5.

Question

The figure shows a wave on a string approaching its fixed end at a wall. When the wave reaches the wall and is reflected, a standing wave is set up in the string. One will observe a node at position
A) 1. 
B) 2. 
C) 3. 
D) 4. 
E) 5.

Quizplus · Accepted Answer

A standing wave is formed due to the superposition of the incident wave and the reflected wave. At the fixed end, the amplitude of the reflected wave is zero, which means there must be a node (a point of zero displacement) at the fixed end. The standing wave formed will have antinodes at positions where the amplitude is maximum and nodes at positions where the amplitude is zero. In this case, there will be a node at the fixed end (position 1), and also at the position where the incident wave and the reflected wave perfectly cancel out, which is 1/4th of the wavelength from the fixed end. Therefore, the node will be at position 3.

The Figure Shows a Wave on a String Approaching Its