1-12 Resonance

Vibrator generates
the wave.

Phase difference between any two
consecutive  right-going waves = 0.00 p rad.

Click and drag the red line to change the frequency of the vibrator.

As the wave travels and is reflected back and forth, it loses its power, for example, because of imperfect reflections or because of friction. Losses will make the amplitude of the wave smaller and smaller. Because of this, at resonance, the amplitude will reach some maximum value and, hopefully, will not reach a value that may exceed the string elastic limit, resulting in a permanent damage of the string.

More reflections at the wall and the vibrator.

The wall reflects the wave.

The vibrator reflects the wave.

When the right-going waves are not in phase, the left-going waves, also, are not in phase. Their interference results in waves with small amplitudes. In this case, we do not have resonance.

At resonance, the right-going waves are in phase as well as the left-going waves. The right-going waves interfere constructively to produce a wave with a very large amplitude.  This is also the case for the left-going waves.

The shape of the wave that you will see on the string is the sum of all right-going  and the left-going waves.

Similarly, we may add all the left-going waves to form a resultant wave moving to the left.

We may add all the right-going waves to form a resultant wave moving to the right.

Let us follow the sinusoidal wave as it travels on the string.

The wall reflects the wave.

The wall reflects the wave.

The vibrator reflects the wave.