The decibel (dB) is a logarithmic unit expressing the ratio of one value to a reference. Decibels compress extremely large ranges (sound can span 13 orders of magnitude) into manageable numbers. A 20 dB increase in sound doesn't mean twice as loud — it means 10 times the pressure ratio. Understanding the conversion between decibels and linear ratios is essential in acoustics, electronics, and communications.
The Formula
For pressure or amplitude ratios:
Decibels = 20 × log₁₀(Ratio)
Ratio = 10^(Decibels / 20)
For power or intensity ratios:
Decibels = 10 × log₁₀(Ratio)
Ratio = 10^(Decibels / 10)
The difference is because power is proportional to amplitude squared, so the factor changes from 20 to 10.
Worked Example: Sound Pressure
A sound is measured at 94 dB (a motorcycle). What is the pressure ratio relative to the reference (20 micropascals, threshold of human hearing)?
Ratio = 10^(94 / 20) = 10^4.7 = 50,118
The sound pressure is about 50,000 times higher than the reference level.
Common Decibel Values
| dB | Maana | Uwiano |
|---|---|---|
| 0 | Sawa na kumbukumbu | 1:1 |
| 6 | Amplitude mara mbili | 2:1 |
| 10 | 10 × amplitude | 10:1 |
| 20 | 100 × amplitude | 100:1 |
| 40 | 10,000× amplitude | 10,000:1 |
| 60 | 1 milioni × amplitude | 1,000,000:1 |
Every 6 dB increase roughly doubles amplitude; every 10 dB roughly doubles power.
Sound Level Examples
| Sauti | dB | Uwiano kwa Kizingiti |
|---|---|---|
| Kizingiti cha kusikia | 0 | 1 |
| Whisper | 30 | 1,000 |
| Mazungumzo ya kawaida | 60 | milioni 1 |
| Pikipiki | 94 | milioni 50 |
| Injini ya ndege | 140 | trilioni 10 |
Kiwango ni cha logarithmic, kwa hivyo kila hatua ya juu inawakilisha ongezeko kubwa la nishati halisi ya sauti.
Attenuation na Faida
Katika umeme, dB chanya inaonyesha ukuzaji (faida), dB hasi inaonyesha kupunguzwa (kupunguza):
- +20 dB faida: Mawimbi 10× kubwa
- -20 dB attenuation: Mawimbi 1/10 ya awali
- -3 dB: Mawimbi yamepunguzwa hadi takriban 70% (nusu ya nishati)
#Vidokezo
Kumbuka utawala wa 3-6-10: 3 dB ≈ √2 (1.4 ×), 6 dB ≈ 2 ×, 10 dB = 10 ×. Kwa sauti, zingatia ukweli kwamba sauti ya sauti hailingani na kipimo cha decibel - 10 dB zaidi kuliko kunong'ona haifanyi pikipiki 10× "sauti zaidi" kihisia; ni makubwa zaidi.
Tumia Decibel to Ratio Converter kubadilisha kati ya desibeli na uwiano wa mstari papo hapo.