Intensity
Power is a measure of work per unit of time, and is measured in watts. For example, audio amplifiers are described by their maximum power
output (e.g., ``30 watts peak power'').
In studying hearing or speech our interest is usually not in the total power of a sound source, but in the power per unit of area,
the Intensity, as in watt/m2. This is because the
human ear offers a fixed area (the ear drum) for detection of sounds in the environment. Intensity is the amount of energy
transmitted per second over an area of a square meter.
The sound intensities that human ears are sensitive to are very small compared to a watt, but
still very wide between the weakest sound detectible and the strongest that does not cause
pain (or damage the ear). Since the watt itself is far too large, the reference level of intensity that all others are
compared to is, by convention, 10 -12 watts/m 2 . This
intensity was chosen as the standard reference level because it is approximately the weakest intensity of a pure tone at 1000 Hz
that can be detected by human listeners, that is, an auditory threshold. The most
intense audio signal that is not painful is roughly 10 watts/m2. Since the most intense is
10 12 or 1,000,000,000,000 (a trillion times) larger than the
threshold level sound, it clearly makes sense to use a logarithmic scale to discuss sound intensity.
The Bel and Decibel
For this reason, the Bel (named after A. G. Bell) was defined this way,
number of Bels = log10 Ix
/ Ir
where is Ix the signal being described and Ir
is a signal used as a reference level. The Bel can be used to compare the relative
intensities of any two signals, e.g., the input and output of an acoustic filter. When a relatively `absolute' description of
the intensity of a signal is needed (like if you want to say `how loud' the background noise in a room is),
the reference level, Ir , is taken to be
10 -12 watts/m 2 . This measure is said to be
an Intensity Level or IL.
But each incremental unit in the Bel scale, from 1 to 2 or from 5 to 6, corresponds to a factor of 10 in intensity. As we said,
the total range that is relevant for human hearing is thus 12 Bels. But a smaller unit would be more manageable when
most practical comparisons are made. Thus the decibel, or dB was defined as one tenth of a
Bel:
Intensity Level in dB = 10 log 10
Ix / Ir
So the weakest audible sound is roughly 0 dB IL and a whispered voice is 1000 times more intense or
30 dB higher. A loud rock concert, close to the threshold of pain might have an intensity ratio of
1012 , or 120 dB IL (relative to the standard reference level).
Pressure
It turns out that a measure of sound pressure is often more useful than intensity. (For one thing, microphones
basically `measure' sound pressure, and instantaneous pressure is the `amplitude' axis in a typical waveform plot.) But sound
pressure is proportional to the square root of the intensity. And conversely, intensity is proportional to the pressure
squared. That is, I = P2 . Thus,
n dB = 10 (Px / Pr )2
Now since log ab = b log a , it follows that
n dB = 20 (Px / Pr)
When pressure is measured in dB, with respect to the standard reference level mentioned above, it is called
`dB sound pressure level' or dB SPL. This is probably the most common `absolute'
measure of sound level. And is closest to what most lay people think the term ``dB'' means.
The following table (based on Moore, 1989) shows some relationships between intensity ratios, pressure ratios and the
standard reference level. Sound levels in dB SPL are expressed relative to a reference intensity level of
10 -12 W/m 2.
Sound level | Intensity ratio | Pressure ratio | Example |
dB SPL | I / Ir | P / Pr | |
140 | 1014 | 10 7 | Gunshot at close range |
120 | 10 12 | 10 6 | Loud rock show |
100 | 10 10 | 10 5 | Shouting at close range |
80 | 10 8 | 10 3 | Busy city street |
70 | 10 7 | 3.16 x 10 3 | Normal conversation |
50 | 10 5 | 316 | Quiet conversation |
30 | 10 3 | 31.6 | Soft whisper |
20 | 10 2 | 10 | In the woods at night |
6.5 | 4.5 | 2.1 | Mean absolute threshold at 1 kHz |
0 | 1 | 1 | Reference level |