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Simple versus Complex Sounds.docx

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McMaster University
Paul Faure

September 20 , 2013 Psych 3A03: Acoustics Simple versus Complex Sounds Sound Attenuation by Radiation - A point source transmits sound energy as an ever expanding spherical wave front - Acoustic power is radiated equally in all directions - As sound sphere expands, the total energy emitted from the source becomes distributed over an exponentially increasing spherical surface area (SA) 2  Surface area of sphere = 4πr - Distance from the sound source can aid us to measure the amplitude to measure the surface area of a sphere - The total power (watt) of the source equals the intensity times the sphere’s surgace area (I x SA)  Power = I4πr 2 Spherical Spreading - Inverse square law. The amount of energy per square meter on a sphere’s 2 surface decreases by 1/r (r = radius of sphere) - Energy at twice the distance from the source is spread four times the area and thus has one-quarter the intensity - Intensity at surface of sphere: Inverse Square Law and Decibels - At 2x distance from source (2r), intensity is ¼ that at source distance (r). Intensity is related to power by:  , (W = power in watt) - Intensity is related to pressure: Intensity proportional to pressure 2 - At 2r pressure will be √(¼) or ½ that of the source  dB = 20log [10/P x ref  dB = 20log [102]  dB = -6.02  At twice the distance the pressure will be 6dB less - Sound pressure level decreases by 6dB for each doubling of distance (dd) from a spherical point source Spherical Spreading: Inverse Sauqre Law - Loss in energy follows inverse square law - Relative sound intensity is proportional to the reciprocal of relative change in distance squared  , where  d x new distance  d = reference distance ref  Can now calculate for any changing relationship Inver Square Law and Decibels - Relative sound intensity is proportional to the reciprocal of relative change in distance squared I 1/[d xd ]refwhere: d = xew distance and d ref= reference distance - dB equation for intensity is: 2  dB = 10log 10/(d
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