# Standing Waves

## Standing Waves

Standing waves (also known as stationary waves) are set up as a result of the superposition of two waves with the same amplitude and frequency, travelling at the same speed, but in opposite directions.

The waves are moving, but the same places have a very large amplitude oscillation while others have zero amplitude and continuous destructive interference.

Stationary waves may be set up when a wave reflects back from a surface and the reflected wave interferes with the wave still travelling in the original direction.

Look at this diagram. Notice that when a wave reflects, it comes back inverted (for example a crest becomes a trough).

The reflected wave and the incoming wave interfere. For example, at the reflecting surface the two waves are always exactly equal and opposite - so they always cancel out. Such a place is called a NODE. At other points along the waves, the two ways always are the same - so they add together or interfere constructively and make a double size wave. Such points are called ANTINODES.

A - places where the waves interere constructively and make double height wave - ANTINODE.

N - places where the two waves always 'cancel' out so there is no movement.

The distance between two NODES or between two ANTINODES is half a wavelength.

The distance between a NODE and the next ANTINODES is one quarter of a wavelength.

#### Harmonics and Overtones

Depending on the wavelength of a wave, different numbers of waves will fill in a certain space. This can be really useful. Lets use an example of a string from a musical instrument.

The lowest possible frequency standing wave that can fit on the string will be:

This is called the fundamental frequency, and it is the longest wavelength for that string. Wavelength will = 2 x L.

If we increase the frequency and decrease the wavelength, the next wave that will fit will be:

This is called the 1st overtone, or the 2nd harmonic. The wavelength = L. And so on...

Did you know that scientists use standing waves to imagine the movement of electrons in atoms?

Imagine a fundamental standing wave inside a box, the dimensions of the box will change the wavelength and frequency of the wave. Now imagine an electron as a standing wave inside of an atom. The dimensions of the atom will affect the movement of the electron!

Note: You will need to be able to describe ways of producing standing waves on strings, with sound waves and with microwaves.

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