Standing waves

Posted in Physics, Waves

Standing (or stationary) waves are waves where the positions of the peaks and troughs do not move. You can observe standing waves by fixing one end of a piece of rope to a stationary object and oscillating it like a sin wave. When the wave reaches the fixed when it 'reflects' back towards you. When this occurs fast enough you'll start to see standing wave patterns like the diagram below.

Standing wave

By changing the frequency different patterns can be observed:

Standing wave A Standing wave B

As mentioned standing waves get their name because they do not appear to move. What is actually happening is that two identical waves are travelling in opposite directions because of the fixed end(s).

Nodes and antinodes

In the context os standing waves, a node is a point where the amplitude is zero. An antinode is the opposite: a point where the amplitude is at its maximum:

Nodes and antinodes

Wavelengths

By looking at the standing wave patterns you can calculate the wave lengths of the standing waves. One of the most simple standing waves (above, left) has two nodes and a single anti mode. The wave length is Dynamic image 0 long, that is the wave length is twice the distance between the two fixed walls.

The addition of another node and antinode pair increases the wave length by Dynamic image 0.

Standing waves in tubes

Standing waves can be created in tubes with either one or no closed ends. The patterns for such standing waves look like so:

One closed end:
Standing wave in pipe with closed end
Open ends:
Standing waves in open pipe

The standing wave patterns in such instances are slightly different to those already described but the physics is the same and the wave length increases by the same amount with each pair of nodes and antinodes.