Fundamentals of Sound
What sound is, and the strange logarithmic scale we measure it on.
Acoustics begins with physics. Sound is a longitudinal pressure wave needing a medium, travelling at about 343 m/s in air. We measure it on the decibel — a logarithmic scale that makes its arithmetic counter-intuitive: two equal sources add to +3 dB, and sound falls 6 dB per doubling of distance. Learn the decibel, the inverse-square law and how the ear hears.
Learning objectives
By the end of this lesson, you will be able to — mapped to the course outcomes for Acoustics in Architecture:
Describe sound as a longitudinal pressure wave and its properties.
Define the decibel and the sound pressure level.
Apply the inverse-square law and the rules for adding decibels.
Explain human hearing and the A-weighted decibel (dBA).
What sound is
Sound is a longitudinal wave needing a medium, with frequency, wavelength and amplitude, travelling ≈ 343 m/s in air.[1, 4]
A pressure wave
SOUND is a LONGITUDINAL mechanical pressure wave — air particles oscillate back and forth (compressions and rarefactions) along the direction of travel — and it NEEDS A MEDIUM (no sound in a vacuum). Its properties: FREQUENCY (f, in hertz — cycles per second, heard as pitch), WAVELENGTH (λ), AMPLITUDE (heard as loudness) and PERIOD (T = 1/f), related by c = f·λ. The audible range is 20 Hz to 20 kHz, narrowing with age.[1, 4]
The decibel & the ear
SPL = 20·log(p/p₀); two equal sources add to +3 dB (not double), sound falls 6 dB per distance-doubling, and the ear's response gives the dBA.[1, 4]
A logarithmic ratio
Sound pressures span a million-to-one range, so we use the logarithmic DECIBEL. The SOUND PRESSURE LEVEL is SPL = 20·log₁₀(p/p₀), with the reference p₀ = 20 µPa (the threshold of hearing). The factor is 20 (not 10) because power goes as pressure squared. Rough values: a whisper ~30 dB, conversation ~60 dB, busy traffic ~80 dB, the threshold of pain ~120–130 dB.[1, 4]
At a glance
| Aspect | One | The other |
|---|---|---|
| Wave & medium | Longitudinal pressure wave | Needs a medium — none in a vacuum |
| Pitch vs loudness | Frequency (Hz) → pitch | Amplitude → loudness |
| The decibel | SPL = 20·log(p/p₀), p₀ = 20 µPa | Logarithmic — a million-to-one range tamed |
| Adding sources | Myth: two equal = double / +6 dB | Reality: +3 dB (double the power) |
| Distance | Inverse-square: −6 dB per doubling | ≈ +10 dB to sound 'twice as loud' |
Key terms
A wave whose particles oscillate along the direction of travel — sound is one; it needs a medium.
Cycles per second — heard as pitch; the audible range is 20 Hz to 20 kHz.
≈ 343 m/s in air at 20 °C; rises ~0.6 m/s per °C; far faster in solids.
A logarithmic ratio for sound level; SPL = 20·log(p/p₀), p₀ = 20 µPa.
Sound from a point source falls 6 dB per doubling of distance.
Two equal sources add to +3 dB (double the power), not double the level.
A decibel filtered to mimic the ear's frequency response — the metric of noise law.
Curves showing the ear is most sensitive around 2–5 kHz, least at low frequencies.
Studio task
Estimate the level at 8 m from a 70 dB source 2 m away using the inverse-square law; then work out the combined level of three identical 65 dB machines (remember the +3 dB rule applies pairwise).
Self-assessment
1. Two identical machines, each 60 dB, running together produce about —
2. By the inverse-square law, doubling your distance from a point source changes the level by —
3. Environmental noise is measured in dBA because —
Recap
References & further reading
- [1]Leslie L. Doelle, Environmental Acoustics. McGraw-Hill, 1972.
- [4]F. Alton Everest & Ken Pohlmann, Master Handbook of Acoustics. McGraw-Hill.
Further reading
- Leslie L. Doelle, Environmental Acoustics. McGraw-Hill.
- M. David Egan, Architectural Acoustics. J. Ross Publishing.
- F. Alton Everest, Master Handbook of Acoustics. McGraw-Hill.
Sources gathered and fact-checked June 2026. Published values vary by source, sample and method — treat as indicative and confirm against the cited standard before structural use.