ETM Learn · 06 / 08
Follow direct sound, early reflections and the later tail.
A handclap reaches your ears along several paths. Direct sound takes the shortest unobstructed route; reflections from surfaces take longer ones. When many reflections crowd together, you can hear a decaying tail rather than separate echoes.
Arrival time tells you when a reflection reaches you. Decay describes falling energy. Size changes path lengths; absorption removes energy at reflections. A larger room need not decay longer. controls dry/wet balance. Start with a click, then change size and absorption separately.
Dotted terms offer a definition on hover, keyboard focus or tap. Click to keep it open; Escape or an outside click closes it. All definitions are also available here.
Time for a 60 dB decay. In a real room it depends on frequency and measurement method; here it is a model estimate.
Adding delayed, weighted copies of the signal according to an impulse response. Describes a linear time-invariant system.
The blend of dry and processed signal. Changing it is not the same as physically moving source or listener in a room.
Use the click. Change one dimension, then absorption with dimensions fixed. Separate arrival time from decay time.
Predict → change one control → compare → explain the result.
Mix changes the dry/wet blend. Physical distance additionally changes timing, direct level and reflection geometry; it is not identical to Mix.
Room, plate and spring are illustrative algorithms, not calibrated physical devices. A real spring is dispersive; a simple chirp’s direction alone is not a complete model.
With linear reverb and fixed routing, does lowering the source change dry/wet ratio?
Linearity means input gain scales both paths equally. Changing send level or distance is another experiment.The image-source method mirrors sources across boundaries to calculate path lengths. Reflection delay relative to direct sound is (Lreflection−Ldirect)/c and depends on the full geometry. For one reflection, . Complete cancellation requires equal magnitudes and opposing phase; weaker reflections give finite notches.
For a diffuse field with uniform mean absorption α and negligible air absorption, Eyring gives ≈ 0.161V/[−S ln(1−α)] in seconds with SI dimensions. At low absorption, Sabine gives 0.161V/(Sα). These estimates depend on assumptions, especially at low frequencies or with uneven absorption. T20/T30 extrapolate a 60 dB decay time from shorter fitting ranges.
For LTI reverb, . uses an impulse response; delay networks construct a response through routing and feedback. This lab combines calculated early paths and a modelled tail. Diffusion, damping and frequency-dependent decay are related, not identical.
τ = (Lreflection − Ldirect) / c
Subtract the direct path length from the reflection path length, then divide by sound speed. An extra 3 metres at 343 metres per second gives about 8.75 ms.
y[n] = Σ h[k]x[n−k]
For each delay k, take input sample x[n−k], multiply by impulse-response weight h[k], then sum. y[n] is the output sample. This assumes a linear time-invariant system.
H(f) = 1 + a·exp(−j2πfτ)
Direct sound is normalized to 1. The reflection has relative amplitude a and delay τ; the complex exponential describes the resulting phase at frequency f. Add the paths to obtain the combined response. Complete cancellation requires equal magnitudes and opposing phases.
T60 ≈ 0.161V/[−S ln(1−α)]
V is room volume in cubic metres, S surface area in square metres and α mean absorption coefficient. ln is natural logarithm. Divide 0.161 times volume by the denominator to obtain seconds. Assumptions include a diffuse field, uniform mean absorption and negligible air absorption; 0<α<1.
T60 ≈ 0.161V/(Sα)
Divide 0.161 times room volume by surface area times mean absorption, using SI units. This is a low-absorption approximation under diffuse-field assumptions, not an exact prediction for every room, especially at low frequencies or with uneven absorption.
Use the path difference, not the reflected path alone.
(5−2)/343 × 1000 = 8.7464 ms. Its absolute arrival after emission is 5/343 = 14.5773 ms. Those are different time references.
First find the residual amplitude |1−0.5|, then convert to dB.
20 log₁₀(0.5) = −6.0206 dB. The notch is finite; complete cancellation requires equal amplitudes. For delay τ, neighbouring comb notches are spaced 1/τ apart in frequency, for this one-reflection, frequency-independent-gain model.
Further reading: Allen & Berkley: image method, 1979