Page 62 - The Master Handbook Of Acoustics

37
SOUND LEVELS AND THE DECIBEL

80
75
( )
10
10
Difference dB = 10 log 10 – 10
= 78.3 dB
In other words, combining the 78.3 dB level with the 75 dB level gives
the combined level of 80 dB.

Ratios and Octaves

An octave is defined as a 2:1 ratio of two frequencies. For example,
middle C (C4) on the piano has a frequency close to 261 Hz. The
next highest C (C5) has a frequency of about 522 Hz. Ratios of fre-
quencies are very much a part of the musical scale. The frequency
ratio 2:1 is the octave; the ratio 3:2 is the fifth; 4:3 is the fourth, etc.
Because the octave is very important in acoustical work, it is well to
consider the mathematics of the octave.
As the ratio of 2:1 is defined as the octave, its mathematical
expression is:

f 2 n
=2 (2-6)
f 1

in which:

f 2 = the frequency of the upper edge of the octave interval.
f 1 = the frequency of the lower edge of the octave interval.
n = the number of octaves.

For 1 octave, n = 1 and Equation (2-6) becomes f 2/f 1 = 2, which is the
definition of the octave. Other applications of Equation (2-6) are now
explored:

Example
The low-frequency edge of a band is 20 Hz, what is the high-frequency
edge of a band 10 octaves wide?

f 2 10
=2
20 Hz
10
f 2 = (20) (2 )
f 2 = (20) (1,024)
f 2 = 20,480 Hz