What is acoustics?
Acoustics is the study of sound. Sound is a vibration that travels as a longitudinal wave through air, water or solids. In air at 20 °C it travels at about 343 m/s.
- Frequency (f): vibrations per second, in hertz (Hz). Humans hear about 20 Hz to 20,000 Hz.
- Wavelength (λ): length of one wave. v = f λ.
- Amplitude: size of the vibration. Bigger amplitude = louder.
Sound in a room: direct sound, reflections, echo and reverberation
In a room the ear gets the direct sound first, then many reflections from walls, floor and ceiling.
- Echo: a reflection we hear as a separate repeat. It needs a delay of at least about 0.1 s, so the wall must be at least about 17 m away (343 × 0.1 ÷ 2).
- Reverberation: many quick reflections that blend together, so the sound "hangs" in the room.
- Reverberation time (T or RT60): the time for the sound level to fall by 60 dB after the source stops.
Good values: about 0.5–1 s for classrooms and speech, 1.5–2.2 s for concert halls.
Try it
Clap once in a bathroom and once in a bedroom with a bed and curtains. Which ring lasts longer? Then use the sliders in the 3D room.
Absorption and Sabine's formula
Each surface has an absorption coefficient α from 0 (reflects everything) to 1 (absorbs everything, like an open window). Concrete ≈ 0.02, carpet ≈ 0.3, acoustic foam ≈ 0.8.
Total absorption A = Σ α S (in m², called sabins). Sabine's formula:
T = 0.161 × V ÷ A (V = room volume in m³, T in s).
So a bigger room rings longer, and adding soft materials makes the ringing shorter.
Resonance and standing waves in rooms
Every object and every room has natural frequencies. If a sound has the same frequency, the vibrations grow large: this is resonance. A wine glass can shatter from a matching note.
Between two parallel walls a distance L apart, sound can form standing waves (room modes) at f = n v / (2L). Some bass notes then sound too strong at some spots and weak at others. Studios use bass traps and non-parallel walls to fix this.
How we hear: decibels, pitch, timbre (psychoacoustics)
Psychoacoustics studies how the brain feels sound.
- Loudness is measured in decibels: L = 10 log₁₀(I / I₀), with I₀ = 10⁻¹² W/m². +10 dB means 10 times the intensity; it sounds about twice as loud. +3 dB means double the intensity.
- Typical values: whisper 30 dB, talk 60 dB, traffic 80 dB, rock concert 110 dB. Long exposure above 85 dB can damage hearing.
- Pitch depends mainly on frequency. Doubling the frequency gives the same note one octave higher.
- Timbre (tone quality) depends on the mix of overtones. That is why a sitar and a flute playing the same note sound different.
Audio tools: microphones, digital audio, software and MIDI
- Microphone: turns sound pressure into an electrical signal. A dynamic mic uses a coil moving in a magnet; a condenser mic uses a moving plate of a capacitor. A speaker does the reverse.
- Digital audio: an audio interface measures the signal many times a second (sample rate, e.g. 44,100 Hz) with a fixed number of bits (bit depth, e.g. 16 bits). The sample rate must be more than twice the highest frequency (Nyquist rule).
- File size (uncompressed) = sample rate × bit depth × channels × time. MP3 and AAC compress it by removing sounds we barely hear.
- Software: a DAW (digital audio workstation) records and edits tracks; a sequencer arranges notes; notation software prints sheet music.
- MIDI: a protocol that sends instructions (which note, how hard, when) between keyboards and computers. It contains no sound; a synthesizer turns it into sound.
Key formulas and definitions
- v = f λ (speed of sound, ≈ 343 m/s in air at 20 °C)
- Echo: minimum distance d = v t / 2 with t ≈ 0.1 s
- T = 0.161 V / A (Sabine reverberation time)
- A = Σ α S (total absorption, m²)
- L = 10 log₁₀(I / I₀), I₀ = 10⁻¹² W/m²
- Room mode: f = n v / (2L)
- Audio size = sample rate × bit depth × channels × time
Worked examples
1. A note has frequency 440 Hz. Find its wavelength in air (v = 343 m/s).
λ = v / f = 343 / 440 = 0.78 m.
2. You shout and hear the echo from a cliff after 2.0 s. How far is the cliff?
The sound goes there and back: d = v t / 2 = 343 × 2.0 / 2 = 343 m.
3. A classroom is 10 m × 6 m × 3 m. Total absorption A = 36 m². Find the reverberation time.
V = 10 × 6 × 3 = 180 m³. T = 0.161 × 180 / 36 = 0.81 s. Good for speech.
4. The same room has bare walls with A = 9 m². What is T now, and what is the fix?
T = 0.161 × 180 / 9 = 3.2 s, far too boomy. Add carpet, curtains or panels to raise A to about 30–40 m².
5. One machine makes 70 dB. What is the level of two identical machines together?
Two machines = double intensity. L = 70 + 10 log₁₀2 = 70 + 3 = 73 dB (not 140 dB).
6. Find the size of a 1-minute stereo recording at 44,100 Hz and 16 bits.
44,100 × 16 × 2 × 60 = 84,672,000 bits ÷ 8 = 10,584,000 bytes ≈ 10.6 MB.
Common mistakes
- Adding decibels like normal numbers: 60 dB + 60 dB is 63 dB, not 120 dB.
- Calling every reflection an echo. An echo needs a delay of about 0.1 s; quick blended reflections are reverberation.
- Thinking soundproofing and absorption are the same. Absorbing panels reduce echo inside; stopping sound passing through walls needs heavy, airtight walls.
- Thinking a MIDI file contains recorded sound. It only contains note instructions.