Question

You and a friend create a standing wave with a rope, then you both hold your hands still while the standing wave continues oscillating. In total, there are 4 nodes in this wave. How many anti-nodes are there?

Answer 1

A standing wave with 4 nodes will have 3 anti-nodes.

Step-by-step explanation:

Nodes are points in the wave where there is no displacement, while anti-nodes are points of maximum displacement. In a standing wave, nodes and anti-nodes are formed due to interference between two waves of the same frequency traveling in opposite directions.

Nodes appear at integer multiples of half wavelengths, while anti-nodes appear at odd multiples of quarter wavelengths. In this case, the wave with 4 nodes will have 3 anti-nodes, as 4 is an even number and the number of anti-nodes is always one less than the number of nodes.