This article takes place in our Acoustic 101 serie!

A Tenth of a Bel

We are still talking here about “Bell telephone laboratories”. Bell engineers needed a reliable metric to develop their new telephone devices. So they created the decibel, or one tenth of a Bel – named in honor of their venerable boss, Alexander Graham Bell.

The human ear is not directly sensitive to pressure variations but rather to power variations of the effective pressure. Also, the perception scale is a logarithmic scale. The pressure level in decibels is calculated according to the following formula:

with Prms, the root mean squared pressure and P0, the reference pressure which corresponds to the threshold of perception at 1000 Hz, ie 0.00002 Pa. An acoustic wave having an effective pressure of 1 Pa will have a level of 94 dB.

The logarithmic side of this unit does not simplify its handling. Acousticians are among the rare people for whom 1 + 1 = 4. Why? Because each time we sum the decibel levels of two sources Lp1 and Lp2, we must use the following formula:

Imagine… a Trumpet

If a trumpet emits a sound of 80 dB, 2 trumpets will emit a sound of 83 dB and 10 trumpets will emit a sound of 90 dB.

Now, if we add an eleventh trumpet to the previous ten, the pressure level will only increase by 0.4 dB. This level variation will not be perceptible to the human ear. This is called the mask effect.

A difference of 3 dB will be perceived as a slight variation in sound perception and a difference of 10 dB will be perceived as a doubling of sound volume.

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This article takes place in our Acoustic 101 serie!

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