Fundamentals of Sound
Sound is a longitudinal pressure wave: particles oscillate along the direction of propagation, so sound needs a medium and cannot cross a vacuum. This domain tests whether you can link the physical properties of a wave to what a listener perceives, and whether you can handle the decibel and the wave equation numerically instead of by guesswork.
Wave properties and perception
- Frequency (Hz) sets pitch; amplitude sets loudness; harmonic content and envelope set timbre.
- Hearing spans roughly 20 Hz to 20 kHz, widest in youth and narrowing with age.
- Speed of sound in air is about 343 m/s at 20 °C; faster in warm air, far faster in water and solids.
- Wave equation: v = f × λ, so λ = v / f, and period T = 1 / f.
- Phase describes the time offset between two waves; equal waves in phase add, opposite phase cancels.
The decibel
A decibel is a logarithmic ratio, not an absolute unit. dB SPL uses 20 µPa as 0 dB (threshold of hearing at mid frequencies); about 120 dB SPL is the threshold of pain. In a free field, doubling the distance drops level by 6 dB.
Worked example. Find the wavelength of a 125 Hz tone at 343 m/s, and the level change when a microphone moves from 1 m to 4 m.
- λ = v / f = 343 / 125 = 2.744 m, quoted as about 2.74 m.
- Distance ratio 4 means two doublings, so 6 + 6 = 12 dB reduction. Reasoning shown: state the formula, substitute SI values, then give the answer with units.
Traps that cost marks
- Adding decibels arithmetically: two identical correlated sources give +6 dB, two uncorrelated sources about +3 dB.
- Confusing wavelength with period, or quoting wavelength in seconds.
- Mixing dB SPL (acoustic), dBu (voltage) and dBFS (digital, where 0 dBFS is the ceiling).
- Forgetting that 6 dB doubles pressure but roughly quadruples power.