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Destructive Interference

What happens if you're standing on a line with the two loudspeakers, so that the more distant speaker is 34.4 cm farther away than the closer one as is shown in Figure 3.10?

Figure 3.10: Two loudspeakers arranged so that one is 34.4 cm more distant than the other.
\includegraphics[width=3.5in]{03acoustics/graphics/stereo_02}

Now, we have to consider the wavelength of the sound being produced. A 500 Hz sine tone has a wavelength of roughly 68 cm. Therefore, half of a wavelength is 34 cm, or the distance between the two loudspeakers.

This means that the sound from the farther loudspeaker is arriving at your position 1/2 of a cycle late. In other words, you're getting a high pressure from the closer speaker as you get a low pressure from the farther speaker.

The end result of this effect is that you hear nothing (this is not really true for reasons that we'll talk about later) because the two pressure levels are always opposite each other. This is shown in Figure 3.11.

Figure 3.11: The top two plots are the individual signals from two loudspeakers in time measured at a position where one loudspeaker is half a wavelength farther away than the other. The bottom plot is the resulting summed signal.
\includegraphics[width=2.75in]{03acoustics/graphics/interference_destruct}


next up previous contents index
Next: Beating, Sum and Difference Up: Wave Addition and Subtraction Previous: Constructive Interference   Contents   Index
Geoff Martin 2006-10-15

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