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Physics - Diffraction and interference of sound waves from two sources

Diffraction and interference of sound waves from two sources

Consider the situation where two speakers facing the same direction are
two metres apart. The speakers are in phase, that is, they are producing
exactly the same frequency and their movements are exactly synchronised
with each other. The two speakers are separate sources of sound waves that
diffract at the speaker aperture and then constructively and destructively
interfere with each other. Consider a line drawn perpendicularly from the
midpoint between the speakers. If an observer were to stand at any point on
this line, she would be an equal distance from either speaker. Therefore,
since the speakers are in phase, compressions from both speakers would
arrive simultaneously at the listener's ears, and then half a cycle later
two rarefactions would arrive. Hence constructive interference would occur
and a loud tone be heard. Points where constructive interference occurs are
called antinodal points . The set of these points is called antinodal
lines as shown.

To either side of the central antinodal line lies a set of points where
constructive interference also occurs. If the observer is closer to one
speaker than the by a multiple of a wavelength, two compressions would
arrive at the observer simultaneously. That is, constructive interference
would occur. For example, at point C on the diagram the observer is four
wavelengths from speaker 1 but three wavelengths from speaker 2. That is,
the _Path Difference_ is one wavelength. The path difference is the
difference in the distance from the observer to each of the speakers. For
constructive interference to occur:

Between the antinodal lines lie nodal lines. These mark the set of points
where destructive interference is occurring. Thinking of this in terms of
pressure variation, these are the points where a compression from one
speaker would arrive at the same time as a rarefaction produced by the
other speaker. Point D is a nodal point . It is 3 1/2 wavelengths from
speaker 1 but 3 wavelengths from speaker 2. The sound waves cancel and it
would therefore be quiet at this spot. For destructive interference to
occur:

You must have an awareness of the effects of altering some aspects of this
set-up. For example, if the frequency of the output tone is increased the
nodal lines would be closer together. If the observer is further out from
the speakers, the nodal separation is greater. If the speakers are closer
together, the nodal separation increases.

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