MOD-12TIME & PHASEPAGE 12 OF 14

Acoustic Wavelength, Period & Phase Alignment

Compute full/quarter wavelengths, temperature-adjusted sound velocity, time-alignment DSP delay, and comb-filtering phase summation.

OSC-1: 440 Hz
BENCH PRESETS:
FREQ
20 HzSingle Cycle Period T = 12.50 ms4000 Hz
OFFSET
0 cm33.5 inches (0.20 λ)400 cm
TEMP
0 °CSpeed of Sound c = 343.4 m/s38 °C
FSDSP Digital Clock Sample Rate
DUAL-TRACE PHASE SUPERPOSITION OSCILLOSCOPE (WAVE A + WAVE B = SUM)
Δφ = 71° | Sum: +4.2 dB
● Wave A (Reference 0°)● Wave B (Delayed -71°)● Acoustic Sum A+B (+4.2 dB)
Full Wavelength λ
4.29m
1/4 Wave: 107.3 cm
DSP Alignment Delay
2.48ms
118.8 samples @ 48k
Relative Phase Δφ
71°deg
0.20 Cycles
Acoustic Sum Gain
+4.2dB
Constructive Sum
TECHNICAL MANUAL // MOD-12 REFERENCE SHEET

How It Works & Acoustic Engineering Principles

#wavelength#phase#comb filtering#time alignment#haas effect#subwoofer delay
GOVERNING ELECTRO-ACOUSTIC EQUATIONSI / IMPERIAL VERIFIED
λ = c / f | Δφ = 360° × (Δd / λ) | G_sum = 20·log₁₀| 2 × cos(Δφ / 2) |
λAcoustic full wavelength in air (meters or feet)
cTemperature-compensated velocity of sound: c = 331.3 + (0.606 × T_°C) m/s
ΔφRelative phase angle offset in degrees caused by path difference Δd
G_sumResulting acoustic summation gain (+6.02 dB coherent to -∞ dB cancellation)

Physical Mechanism & Theory

Sound travels through air at roughly 343 meters per second (34.3 cm per millisecond). Because wavelength spans over three orders of magnitude across the human hearing range—from a massive 17.15 meters at 20 Hz down to a tiny 1.71 centimeters at 20 kHz—physical driver offsets affect bass and treble completely differently.

When two coherent signals (such as a subwoofer and main monitors at their 80 Hz crossover frequency, or a direct vocal and a floor bounce) arrive at the listener with a path difference Δd equal to half a wavelength (180° phase shift), they destructively cancel each other. Applying exact DSP time delay (Δt = Δd / c) aligns the acoustic wavefronts back to 0° phase for a +6 dB coherent sum.

Studio Bench Rules of Thumb

  • 01.1 Millisecond ≈ 1.13 Feet (34.3 cm): Memorize this studio constant to quickly convert physical speaker or microphone offsets into DSP milliseconds.
  • 02.48 kHz Sample Offset Rule: At a 48 kHz sample rate, 1 digital sample of delay equals 20.8 microseconds, or roughly 7.1 millimeters of acoustic air travel.