How a Stationary Wave Forms
How a Stationary Wave Forms
- Every wave so far has moved along, carrying energy with it. This one does not move along. But it is not frozen: every point still moves up and down.
- What stays still is the shape. Some points never move, and the points with the largest swing stay in one place. That fixed shape is a (also called a standing wave). It is made by , the same adding rule as before.
Two waves, opposite directions
- Take two identical waves going opposite ways along the same line. Identical means the same type, the same amplitude, the same wavelength and the same speed.
- Where they overlap, add them together. The shape you get does not slide along the line. But every point on it still swings up and down.
- In real life you rarely need two separate sources. Send one wave at a wall and it reflects. The reflection travels back the opposite way, identical to the wave going in, and the two add. So most stationary waves are a wave adding to its own reflection.
The picture over one period
Follow the two waves as they slide through each other over one full period . The pattern repeats the same thing again and again:
| Time | The two waves | The pattern |
|---|---|---|
| Start | line up crest on crest | twice as tall as one wave |
| A quarter period later | one slid left, one slid right, crest on trough | completely flat |
| Half a period | line up again, the other way round | twice as tall, upside down |
t = 0.15 T·pulse factor cos(ωt) = 0.59·pattern is at maximum displacement
Some places are always flat and some always swing the most. Those fixed places never move along the wave. The pattern swings in place but never travels, and that is why we call it stationary.
The exact statement
- Here is the mark-scheme line, word for word: a stationary wave forms when two waves of the same frequency, travelling in opposite directions, superpose.
- Three things earn the marks: same frequency, opposite directions, superpose. The easy one to forget is opposite directions.
Your turn— tap to reveal the worked answer (9702-style)
State the conditions needed for two progressive waves to form a stationary wave.
Answer: the two waves must be the same type, have the same amplitude, the same wavelength (and speed), and travel in opposite directions, so they can superpose. (9702-style)