Valori utili in dB en

From "Physics, Waves, Music": a website about the physics of waves and sound, acoustics of musical instruments, musical scales, harmony and music.

AI-translated from Italian. Original page: Valori_utili_in_dB

Recalling that the measure in dB of the level of a physical quantity I with respect to a reference value I0 is

I(dB)=10log10(II0),

here is a table for converting between the values of a level measured in dB and the corresponding value of the ratio I/I0. If you do not know the meaning of the logarithmic function, visit the page the logarithm function


level of I in dB intensity ratio I/I0 amplitude ratio
−30 dB 1/1000 about 1/32
−20 dB 1/100 1/10
−10 dB 1/10 about 1/3.2
−9 dB about 1/8 about 0.35
−6 dB about 1/4 about 1/2
−3 dB about 0.5 about 0.71
−1 dB about 0.8 about 0.89
1 dB about 1.25 about 1.12
3 dB about 2 about 1.41
6 dB about 4 about 2
9 dB about 8 about 2.8
10 dB 10 about 3.2
20 dB 100 10
30 dB 1000 about 32

The second column holds for quantities proportional to a power, such as sound intensity or electrical power. For amplitudes, such as sound pressure or electrical voltage, the power is proportional to the square of the amplitude and the level is calculated as 20log10(p/p0) (see sound pressure levels): the amplitude ratios are therefore the square roots of those in the second column. For example 6 dB corresponds to an intensity four times larger, but to a pressure only twice as large.

Check your understanding

Problem. A 100 W amplifier replaces a 50 W one. By how many dB does the maximum sound level increase? Solution. The power doubles: 10 log102 dB ≈ 3 dB. A small increase: for a sound that seems about "twice as loud" about 10 dB are needed, that is ten times the power (see perception of loudness).

Problem. A violin produces 60 dB at a certain point. How much do ten violins playing together produce, assuming they all contribute the same intensity? Solution. The intensities of independent sources add: the intensity becomes 10 times larger, so the level increases by 10 dB and becomes 70 dB.

Problem. What intensity ratio corresponds to 23 dB? And what pressure ratio? Solution. 23 dB = 20 dB + 3 dB, so the intensity ratio is about 100 · 2 = 200. The pressure ratio is the square root, about 14 (10 · 1.41).

Further reading and links

"Physics, Waves, Music": a website about the physics of waves, acoustics of musical instruments, musical scales, harmony and music.