02_Decibels

# 02_Decibels - Hearing (and calculating) the Decibel...

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Hearing (and calculating) the Decibel Amplitude is a physical phenomenon; loudness is a perceptual phenomenon. A sound’s amplitude refers to the displacement of the air molecules and the force they bring to bear on the ear’s tympanic membrane. The brain’s response to the different degrees of that force is loudness. The ear/brain combination (hereinafter “ear”) is more sensitive at some frequencies that others, and that topic is treated in a later lab. Regardless of frequency range, the ear responds to ratios of loudness rather than simple differences. The ear responds to a wide range of sound pressures, with an overall sensitivity of 10 12 to 1. Using powers of 10 to divide this giant range (like the Richter scale used to measure the severity of earthquakes) into parts yields the bel scale, and further subdividing each bel into ten ratios gives the decibel. A decibel provides a measure of the relative magnitudes of two things expressed as a ratio. When amplitudes (such as sound pressures or electrical voltages) are expressed as ratios, the formula for the decibel is: 20log(a1/a2) where a1 and a2 are the amplitudes or voltages in question. The logarithm used here is based on powers of 10. The log function answers the question: to what power, including fractional powers, must 10 be raised to equal the number under inspection. For example, consider the log of 100. 100 is the same as 10 times 10, or 10 2 , so the log of 100 is 2,

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## This note was uploaded on 04/04/2011 for the course MUSIC STUD 4711 taught by Professor Brokaw during the Spring '10 term at Temple.

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02_Decibels - Hearing (and calculating) the Decibel...

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