Physics - The superposition of waves
The superposition of waves
It is rarely the case that the sounds we hear are made up of a single
frequency tone. Rather, many of the sounds produced and heard by us are a
combination of a number of sound waves that are interfering with each
other. It is difficult to picture the interference of sound waves and this
situation is often modelled by showing waves travelling in springs.
Consider the diagrams shown below.
The spring shows two pulses, one sent from each end of the spring. They
are equal in size but heading in opposite directions. At the moment when
they overlap, the displacement caused by each pulse is summed. The
principle that describes the behaviour of the spring is called the
principle of superposition . The resultant amplitude is the vector sum
of each of the displacements. Once the pulses pass through one another they
continue on unaffected by the fact that they once interacted.
If a positive and a negative pulse are sent along the spring as shown, at
the point of overlap the displacements would begin to cancel each other
out. Once again the vector sum of the displacements determines the
resultant amplitude. If both pulses were equal in size there would be a
short period in which the resultant amplitude of the spring was zero.
Again, once the pulses have passed through one another they will continue
on unaffected by their interaction.
Whenever two or more transverse or longitudinal waves interfere the net
amplitude is determined according to the principle of superposition.
Examples include waves travelling in guitar strings, echoes bouncing around
a room or the interference of waves from two speakers. This principle can
also be useful in noise reduction.
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