Superposition

The principle of superposition may be applied to waves whenever two (or more) waves travelling through the same medium at the same time.

When 2 waves are in phase phase with each other (the peaks and troughs coincide with each other the effect for the resultant wave is additive.  The example on the left shows the 2 waves which oscillate at 2 units  form the central point at the same time.  When they are superposed, the resultant line is 4 units from the central point.

When the waves are out of phase, the lines above and below cancel out.  This is because the blue wave is at +2 position (above the line) at the peak and the corresponding brown wave is at the -2 position (below the line)





Basically the resultant wave is a bit like a vector sum using the distance from the central point from which it oscillates.  The first time that the resultant red wave crosses the horizontal line marked x, the 2 component waves (blue and grey) can be seen to be equal distances above and below the line.

In some cases more complex wave forms can be produced by 2 component waves.
















Most sounds are not simple.  They are often mixtures of 2 or more "pure sounds" which provide make tones.  2 tones combined will produce a beat.  This is where there is a noticeable change in volume which will make a waahaaw- waahaaw type of sound.  Beat frequency is calculated by:

A beat wave pattern is shown below.



For some use of beats in phone tones try this page.


Many musical instruments produce complex sounds rather than simple pure note.  As a result the wave form is quite sophisticated

Properties of sound waves and the wave equation.

Sound waves are mechanical, that is they require a medium to travel in.  The particles that make up the medium vibrate backwards and forwards in the same direction as the sound is travelling. Keep an eye on the red dots if you don't believe me.  If you are skillful try it with a black dot next.

As shown by the animation above, the movement of particle causes area of high and low pressure.  These are known as compression and rarefaction respectively.

The distance between 2 adjacent compressions, 2 adjacent rarefactions, or a single compression and rarefaction combined is a wavelength of a sound wave.

When represented as a diagram, the compressions are drawn above the horizontal axis and the rarefactions below.

When the amplitude increases on a sound wave diagram the volume increases. As the diagram indicates it gets louder.

In the case of sound, it travels at a fixed value in air (340 m/s).  Thus if you decrease the frequency, the wavelength will increase and the pitch will decrease (more bass).  If you were to reverse this, and increase the frequency you would find that the pitch gets higher (more treble).

Some definitions for waves

Wavelength - The distance between 2 crests, or 2 troughs, or, one complete crest and one complete trough. This can shown graphically by plotting the displacement on the vertical axis of graph and the distance on the horizontal axis.

Amplitude - The strength of the signal produced by a wave.  It is represented by the displacement from the horizontal axis.  The greater the amplitude, the stronger the signal, the brighter the light or the louder the sound.

Crest - the part of the wave at the highest point from central point that it will oscillate around.

Trough - the part of the wave at the highest point from central point that it will oscillate around

Period - the time it takes one wave to pass a set point.  Note that if you graph it now, the horizontal axis is now time, not length.  Period is denoted by the symbol T.

Frequency - the number of waves that will pass a set point in one second.  The units to describe this is Hertz (cycles per second).  If you can imagine all the waves in the figure above are travelling at the same speed, you can see the idea with frequency. Frequency is denoted by the symbol f.  

There is a mathematical relationship between frequency and period.  It is as follows:

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