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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 [1]. 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 [2]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 [3]. 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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