Acoustics - 4

# Acoustics - 4 - Lecture 4 The human ear is sensitive to a...

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Lecture 4

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The human ear is sensitive to a very large range of intensities The psychological sensation of loudness does not have a linear relationship with the physical properties of intensity. Because of the vast range of intensities and the non-linear relationship, the numbers used in measuring the intensity of sound are too large to use To put the intensity scale into manageable numbers, we use a non-linear scale
Any number can be expressed as a power of 10 100 is 10 to the second power of 10 (or 10 2 ) 10,000 is 10 to the fourth power of 10 (or 10 4 ) 10 is the common base & is assumed The logarithms (or log) is exponent that represents how many times we multiply the base

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Linear scale = 10,000,000,000,000 - 1 Log scale = 10 13 - 1 dB scale = 130 – 0 “log” is the exponent Log of 10 4 = 4 Log interval appears linear but each log represents an increasingly larger number
1 10 100 1,000 10,000 100,000 1,000,000 10,000,000 100,000,000 0 10 0 1 10 1 2 10 2 3 10 3 4 10 4 5 10 5 6 10 6 7 10 7 8 10 8

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The amplitude of a sound is its relative intensity To measure intensity, we started with a Bel scale Named after A.G. Bell Bel scale has base of 10 so a sound that is 10x’s greater than another is 1 Bel greater (still too large a scale) Changed to decibel scale (dB) which is 1/10 th of a Bel
dB are units by which the magnitude or strength of a sound are expressed Non-linear scale Each increment represents an increasingly larger difference Why use logs? Ear can hear large range of intensity Up to 10 13 or 10trillion units on a linear scale Logs help us condense this to 130 dB Better approximation of how we judge loudness

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We measure intensity in square centimeters
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