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By David Howard, Jamie Angus

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Extra info for Acoustics and Psychoacoustics, Third Edition

Example text

For the SWL and SIL, because we are adding powers, the results will be the same whether the sources are correlated or not. However, for SPL, there will be a difference between the correlated and uncorrelated results. The main difficulty that arises when these measures are used to calculate the effect of combining sound sources, is confusion over the correct use of decibels during the calculation. 3 Adding decibels together Decibels are power ratios expressed on a logarithmic scale and this means that adding decibels together is not the same as adding the 25 Introduction to sound sources’ amplitudes together.

12. 12 Calculate the increase in the sound pressure level (SPL) when two vocalists sing together at the same level and when a choir of N vocalists sing together, also at the same level. The total level from combining several uncorrelated single sources is given by: PN uncorrelated = P͙N ෆ This can be expressed in terms of the SPL as: ΂ ΃ P P͙N ෆ SPLN uncorrelated = 20 log10 ᎏ ᎏ = 20 log10 ᎏᎏ + 20 log10(͙N ෆ) pref pref ΂ ΃ In this equation the first term simply represents the SPL of a single source and the addition of the decibel equivalent of the square root of the number of source represents the increase in level due to the multiple sources.

If one moves to another point (P2) which is not equidistant, the waves no longer necessarily add constructively. In fact, if the path difference is equal to half a wavelength then the two waves will add destructively and there will be no net pressure amplitude at that point. This effect is called interference, because correlated waves interfere with each other; note that this effect does not occur for uncorrelated sources. The relative phases of the waves depend on their path difference or relative delays.

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