Decibels

In all phases of audio technology the decibel is used to express signal level differences. expressed by the same level, 10 dB. Any 10 dB level difference, regardless of the actual powers involved, will represent a 2-to-1 difference in subjective loudness. We will now expand our power decibel table: P1 (watts) Level in dB.

the decibel (abbreviated dB) is used to express differences between two values signal. The reason the decibel is such a useful measure is that it enables us to use a comparatively small range of numbers to express large and often unwieldy quantities. For convenience, we find the ratio between the two numbers and convert that into a logarithm. . If we measured one value as 10 watt and another as 1000 watt, we say that one is 20 dB greater than the other. If the softest audible sound has a power of about 0.000000000001 watt/sq. meter and the threshold of pain is around 1 watt/sq. meter, giving a total range of 120dB.

Power difference in dB = 10 log ( Power A / Power B)

The following tabulation illustrates the usefulness of the concept. Letting Power B = 1 watt:

Power A (watts) Level in dB
1 0
10 10
100 20
1000 30
10,000 40
20,000 43


The usefulness of all this becomes apparent when we think about how the ear perceives loudness. The decibel also makes sense from a psychoacoustical point of view in that it relates directly to the effect of most sensory stimuli. First of all, the ear is very sensitive. In the second place, our judgment of relative levels of loudness is somewhat logarithmic. If a sound has 10 times the power of a reference (10dB) we hear it as twice as loud. If we merely double the power (3dB), the difference will be just noticeable.

Converting voltage or pressure ratios to decibels

Remember that the dB is used to describe relationships of power. Power is not often conveniently measured, especially in electronic devices. We can use voltage, current, and pressure ratios as they relate to power. Most often we measure voltage and use the formula P = E2/Z to get power. Squaring a value doubles its logarithm, so our dB formula becomes:

Power divergence in dB = 20 log (voltage A / voltage B)

We now present a table useful for determining levels in dB for ratios given in voltage. Letting Voltage B = 1 volt:

Voltage A Ratios Level in dB
1 0
1.25 2
1.60 4
2 6
2.5 8
3.15 10
4 12
5 14
6.3 16
8 18
10 20

Sound Pressure Level (SPL)

For decibels of sound pressure level (SPL), the reference is the extremely low value of 20 x 10-6 newtons/m2. This reference pressure corresponds roughly to the minimum audible sound pressure for persons with normal hearing. SPL ranges from 0 dB SPL (the threshold of hearing), to above 120 dB SPL (the threshold of pain). Conversational speech is about 70dB SPL. A change of 1 dB is about the smallest SPL difference that the human ear can detect, while 3 dB is a generally noticeable step, and an increase of 10 dB is perceived as a “doubling” of loudness. As a convenient point of reference, note that an rms pressure of 1 pascal corresponds to a sound pressure level of 94 dB. We commonly use a sound level meter (SLM) to measure SPL