Sound Converter
Convert between decibels, bels, and nepers for sound and signal level measurement.
Sound level measurement uses the decibel scale โ a logarithmic unit that compresses the enormous range of human hearing into a manageable scale. From the threshold of hearing at 0 dB to a rocket launch at 180+ dB, each increase of 10 dB represents a tenfold increase in acoustic intensity. This logarithmic nature means that understanding decibels requires moving beyond simple arithmetic, but it also makes describing the full range of human-perceptible sounds practical.
Popular Sound Conversions
The Decibel Scale: Logarithmic, Not Linear
The decibel (dB) expresses a ratio, not an absolute quantity. For sound pressure level (SPL), dB = 20 ร logโโ(P / Pโ), where Pโ is the reference pressure of 20 ฮผPa โ the approximate threshold of human hearing. Because it is logarithmic: +3 dB represents roughly double the acoustic power; +6 dB doubles the sound pressure; +10 dB is perceived as approximately twice as loud by the human ear. Conversely, -10 dB sounds about half as loud. Normal conversation occurs around 60 dB; a lawnmower at 1 meter is about 90 dB; a jet engine at 30 meters produces about 140 dB. Prolonged exposure above 85 dB causes hearing damage; sounds above 120 dB cause immediate pain.
| Source | Sound Level |
|---|---|
| Threshold of hearing | 0 dB SPL |
| Quiet whisper | 30 dB |
| Normal conversation | 60 dB |
| Heavy traffic | 85 dB |
| Live concert (front row) | 110โ120 dB |
| Jet engine (30 m) | ~140 dB |
Decibels in Audio Engineering and Electronics
In audio electronics, dB is used as a relative measure of gain or attenuation. Voltage gain in dB = 20 ร logโโ(Vout / Vin); power gain in dB = 10 ร logโโ(Pout / Pin). An amplifier with a gain of 20 dB amplifies voltage by 10ร (power by 100ร). Standard reference levels include dBu (reference 0.7746 V RMS, used in professional audio), dBV (reference 1 V RMS), and dBm (reference 1 mW into 600 ฮฉ, used in telecommunications). Noise floors in high-quality microphone preamps are typically โ130 to โ120 dBu; headphone amplifiers aim for < โ100 dBu THD+N. Understanding which reference a spec sheet uses prevents misinterpreting equipment comparisons.
Sound Speed and Frequency
The speed of sound in air at 20ยฐC (68ยฐF) is approximately 343 m/s (1,125 ft/s or 767 mph). It varies with temperature: roughly +0.6 m/s per ยฐC. At 0ยฐC, the speed is about 331 m/s; at 35ยฐC, about 352 m/s. Speed of sound in water is approximately 1,480 m/s โ over 4ร faster than in air, which is why sonar is effective underwater. The relationship between speed, frequency, and wavelength: wavelength = speed / frequency. A 100 Hz bass note in air has a wavelength of 343 / 100 = 3.43 meters; a 10 kHz treble note has a wavelength of 3.43 cm. This is why bass frequencies require large speakers and room dimensions for proper reproduction.
Further Reading
Sources & References
- NIST โ Units and Conversion Factors โ Official unit conversion factors from the National Institute of Standards and Technology.
- BIPM โ The International System of Units (SI) โ International SI unit definitions from the International Bureau of Weights and Measures.