What happens when a reflected transverse wave meets an incident transverse wave? When two waves move in opposite directions, through each other, interference takes place. If the two waves have the same frequency and wavelength then *standing waves* are generated.

Standing waves are so-called because they appear to be standing still.

Tie a rope to a fixed object such that the tied end does not move. Continuously move the free end up and down to generate firstly transverse waves and later standing waves.

We can now look closely how standing waves are formed. Figure 27 shows a reflected wave meeting an incident wave.

When they touch, both waves have an amplitude of zero:

If we wait for a short time the ends of the two waves move past each
other and the waves overlap. To find the resultant wave, we add the two together.

In this picture, we show the two
waves as dotted lines and the sum of the two in the overlap region
is shown as a solid line:

The important thing to note in this case is that there are some
points where the two waves always destructively interfere to zero.
If we let the two waves move a little further we get the picture
below:

Again we have to add the two waves together in the overlap region to
see what the sum of the waves looks like.

In this case the two waves have moved half a cycle past each other
but because they are completely out of phase they cancel out completely.

When the waves have moved past each other so that they are
overlapping for a large region the situation looks like a wave
oscillating in place. The following sequence of diagrams show what the resulting wave will look like. To make it clearer, the arrows at
the top of the picture show peaks where maximum positive
constructive interference is taking place. The arrows at the bottom
of the picture show places where maximum negative interference is
taking place.

As time goes by the peaks become smaller and the troughs become
shallower but they do not move.

For an instant the entire region will look completely flat.

The various points continue their motion in the same manner.

Eventually the picture looks like the complete reflection through
the xx-axis of what we started with:

Then all the points begin to move back. Each point on the line is
oscillating up and down with a different amplitude.

If we look at the overall result, we get a standing wave.

If we superimpose the two cases where the peaks were at a maximum
and the case where the same waves were at a minimum we can see the
lines that the points oscillate between. We call this the *envelope*
of the standing wave as it contains all the oscillations of the
individual points.
To make the concept of the envelope clearer let us draw arrows
describing the motion of points along the line.

Every point in the medium containing a standing wave oscillates up
and down and the amplitude of the oscillations depends on the
location of the point. It is convenient to draw the envelope for the
oscillations to describe the motion. We cannot draw the up and down
arrows for every single point!

Standing waves can be a problem in for example indoor concerts where the dimensions of the concert venue coincide with particular wavelengths. Standing waves can appear as `feedback', which would occur if the standing wave was picked up by the microphones on stage and amplified.