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# Simple versus Complex Sounds.docx

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McMaster University

Psychology

PSYCH 3A03

Paul Faure

Fall

Description

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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