Audio Reverb and Echo

Clap once in an empty hall and the clap does not stop when your hands do. It keeps going, smeared into a soft roar that fades over a second or two. That fading roar is reverberation, and it is the single most familiar thing a room does to sound.

Most reverb controls hide this behind words like size, space or ambience. They are pleasant words with no units. The one number that rooms, acousticians and reverb designers all share is the decay time, and it can be measured. A reverb that claims a two second decay should produce a tail that falls by sixty decibels in two seconds, and you should be able to check it.

What a room does to a sound

Sound leaves a source in every direction, strikes the walls, floor and ceiling, and comes back many times. The first few returns are distinct reflections. Later ones arrive so densely that no single reflection stands out, and each trip loses a little energy to the surfaces it touches. The result is a tail whose level drops at a steady rate, so many decibels per second.

The standard way to name that rate is T60, the time the sound pressure level takes to fall by 60 dB after the source stops. Sixty decibels is a factor of a thousand in pressure. Measuring a full 60 dB drop is often impractical, so engineers fit a straight line to a smaller drop and extend it. Doubling the time for a 30 dB fall gives the T30 value; tripling a 20 dB fall gives T20.

Reverberation is not echo, although both are reflections. A reflection that returns about 50 to 100 ms after the sound is heard as a separate repeat. Reflections that follow one another more closely than about 50 milliseconds fuse into reverberation. The same physics gives a canyon its echo and a stairwell its wash.

Decay time also depends on frequency. Most rooms absorb less energy at low frequencies, so their low notes ring longer than their high ones. That is why careful measurements are often stated per octave band rather than as one figure, and why a careful reverb treats the highs and the lows differently.

Sabine’s formula and its limits

The science of decay time began with a lecture room that nobody could use. In 1895 the senior physics staff at Harvard considered the acoustics of the new Fogg Lecture Hall impossible to improve, and the job passed down to a young physics professor, Wallace Clement Sabine. He compared it with the Sanders Theater, which people liked, and spent night after night moving materials between the two rooms.

His instruments were organ pipes, a stopwatch and his own ears. He timed how long a tone took to become inaudible after the pipe stopped, a fall of roughly 60 dB. From those timings he found that decay time grows with the size of the room and shrinks as absorption is added. Sabine was also the acoustician of Boston’s Symphony Hall.

His relation is usually written T60 = 0.1611 V / (S a), with the volume V in cubic metres, the surface area S in square metres and a the average absorption coefficient of the surfaces. The constant comes from the speed of sound, about 343 metres per second at 20 degrees Celsius. An absorption coefficient runs from 0 to 1: a thick painted concrete ceiling is close to 0, and a large open window, which reflects nothing back, is 1.

Take the example room in the tool: 20 by 14 by 8 metres, so 2,240 cubic metres of air and 1,104 square metres of surface, with an average absorption of 0.2. Sabine gives 0.1611 x 2,240 / (1,104 x 0.2), or 1.63 seconds. Eyring’s formula, proposed by Carl F. Eyring in 1930, replaces a with the negative logarithm of 1 minus a and gives 1.46 seconds for the same room.

The two estimates disagree because neither is exact. Sabine’s empirical rule fits large, live rooms with little absorption, which is where he did his work. Eyring’s version suits small, heavily treated rooms, and Sabine tends to overestimate those. Both ignore the shape of the room and the uneven placement of absorbers. Treat them as a starting point for a setting, not a prediction of what a microphone would record.

Building a room you can measure

Artificial reverb started as an echo chamber: a recording played into a reverberant room through a loudspeaker and picked up again by a microphone, an approach dating from the 1930s. Springs and steel plates followed in later decades, and digital reverb arrived in 1976. In 1962 M. R. Schroeder described methods for producing, by purely electronic means, artificial reverberation that listeners could not tell apart from a real room. He also noted that echo densities of a thousand per second were not easily achieved by the reverberators of his day.

The algorithmic reverb in the tool uses the two building blocks that work made famous. The first is the feedback comb filter, whose output is its input plus a scaled copy of its own output from K samples earlier. Its response to a click is a train of clicks K samples apart, each smaller than the last by the feedback factor, and the filter is stable only when that factor is below 1.

That impulse train is where the decay time enters, and the arithmetic is short. A loop of d seconds is travelled T60 / d times in T60 seconds. For the train to have fallen by 60 dB, a factor of a thousand, the loop gain must satisfy g to the power T60 / d equals 10 to the minus 3. Solving gives g = 10^(-3d/T60). A 33 millisecond comb with a two second decay needs a gain of about 0.892. Drop the 3 from that exponent and the tail lasts three times as long as requested, which is exactly the mistake the tool’s tests are built to catch.

Eight combs in parallel, with lengths that share no common factor, give many overlapping trains whose clicks rarely line up. Three all-pass filters in series then multiply the echoes further. An all-pass filter passes every frequency at the same gain and changes only the timing between frequencies, so it thickens the texture without colouring the tone. Inside each comb loop a gentle low-pass filter takes a little more from the highs on every trip, the way soft furnishings do.

Convolution reverb takes the other road. It records, or computes, how a space answers a single click, then convolves every sample of the input with that impulse response. The generated response in the tool is decaying noise that reaches -60 dB at the set time, with optional early reflections. Those come from the image method of J. B. Allen and D. A. Berkley, published in 1979: in a rectangular room, every reflection path behaves like a straight path from a mirror image of the source.

Measuring what you made

Here is the useful part. Every reverb in the tool is linear, so it is completely described by its impulse response, and that response can be measured just as a real room’s would be. In 1965 Schroeder showed that integrating the squared response from the end backwards gives, in one pass, the average decay curve that would otherwise take many noisy measurements to find. The curve is smooth, and it shows plainly whether a decay is a clean straight line or not.

The tool draws that curve, fits a line between 5 and 35 dB down, and extends it to -60 dB. Set 2.00 seconds in the example room and the fit, taken in the octave around 500 Hz, lands at 1.99 seconds. Across all frequencies it reads 1.58 seconds, because the damping makes the highs die sooner. Turn damping off and the two numbers agree.

The rendering itself is checked the same way. The browser’s offline audio engine renders the wet signal with a convolver told not to rescale the response, which then performs a plain linear convolution. A separate FFT convolution in a background worker computes the same signal, and the largest difference between the two is printed. In the example it is about two parts in ten million of full scale.

Echo, and keeping a mix clear

Echo is a simpler machine: a delay line whose output is fed back into its input. Each pass makes another repeat, quieter by the feedback amount, and a low-pass filter in the loop makes each repeat a little duller than the last. A ping-pong delay sends the repeats alternately to the left and right channels. With a 330 millisecond delay and 35 percent feedback, the repeats take about 2.17 seconds to fall 60 dB.

Measured decay times for echo come out less tidy. Separate repeats make a staircase rather than a smooth slope, so a fitted line describes them only roughly, and the tool labels that number as approximate. Short delays of 30 to 50 milliseconds give a doubling effect close to double-tracking rather than an echo, and longer ones turn into slapback.

Reverberation changes how a sound’s spectrum is heard but never its pitch, and too much of it costs clarity. Rooms built for speech are kept short because the tail of one syllable can hide the next, until cat, cab and cap sound alike. The same applies to a voice in a mix. A shorter decay, a lower wet level and a little more damping keep words readable, while a longer decay suits slow, sustained music.

None of this replaces a measured room. Sabine and Eyring assume even absorption in a simple box. Real halls scatter, focus and leak sound in ways no formula captures, and the image method here stops after three reflections. What the tool promises is narrower and easier to keep: the decay time you set is the decay time it builds, and the graph shows you the proof.