Sound Volume

Chapter 1. Physical Sound

1.2. Sound Volume

Sound volume is always measured with respect to some reference level and almost never in absolute terms like most other quantities are. Thus, what we think of as “sound volume” is in fact a ratio in sound pressure. The unit measuring sound pressure is the Bel. Because we want to be able to pick out small pressure ratio differences, we do not use the Bel, but the decibel (symbol: dB): 1 dB = 0,1 Bel .

What is the decibel scale?

Since the dB is a relative scale, we need a reference. The softest sound a human can hear is defined as 0 dB SPL (equivalent to air pressure of 20 µPa) where SPL stands for Standard Pressure Level. Because sound pressure ratios span over a very large span of values, the dB scale is logarithmic; this means that the space between 1 and 10 is the same as the space between 10 and 100; this allows displaying much larger scales in a convenient manner (see Table 2 below). The choice of a logarithmic scale also has a physiological reason: the ear itself has logarithmic sensitivity.

Air pressure ratio r Intensity ratio I
100000 = 105 100 dB
10000 = 104 80 dB
1000 = 103 60 dB
100 = 102 40 dB
10 = 101 20 dB
~2 6 dB
1 0 dB
~0.5 -6 dB
0.1 = 10-1 -20 dB
0.01 = 10-2 -40 dB
0.001 = 10-3 -60 dB
0.0001 = 10-4 -80 dB
0.00001 = 10-5 -100 dB

Table 2 Amplitude Ratios and Their dB Equivalent

The equation linking the sound wave amplitude ratio r with the pressure ratio I (in dB) is defined as:

Equation3 Logarithmic relationship between the pressure ratio and the sound volume

Equation 3 Sound and Intensity Amplitude Ratios

For example, if the pressure at some location is one hundred thousand times larger than that at some other location, we will say that there is a one hundred decibel difference in pressure; if the pressure is twice as high, there is a six-decibel difference. Conversely, if the pressure difference is half, we will say that there is a negative six decibel difference: the logarithmic scale transforms multiplication and division into addition and subtraction.

 

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