When an acoustic consultant measures a room, the raw data is noisy, spiky, and nearly impossible to interpret by eye. The impulse response shows thousands of reflections overlapping in complex patterns. To extract a clean RT60 value from this chaos, we need a way to see the overall trend of energy decay over time. That tool is the decay curve — and understanding it is essential to understanding how reverberation time is actually measured.
TLDR
A decay curve (also called an energy decay curve or EDC) is a graph showing how the total sound energy in a room decreases over time after a sound source stops. The x-axis is time (in seconds) and the y-axis is energy level (in decibels). A straight line on the decay curve means the room decays uniformly — the steeper the line, the shorter the RT60. A curved or kinked line indicates non-uniform decay (common in coupled spaces or rooms with uneven absorption). RT60 is extracted by fitting a straight line to the decay curve and measuring the time it takes to cross a 60 dB range. Modern practice uses the Schroeder backward integration method (ISO 3382-2 Annex B) to generate the decay curve from an impulse response, which produces smoother, more repeatable results than direct squared-impulse methods.
Real-World Analogy
Imagine watching a sparkler on New Year's Eve. When you first light it, sparks fly in all directions — bright and chaotic. As the sparkler burns down, the sparks get fewer and dimmer, but at any given instant you might see a bright flash or a dim moment. If you took a long-exposure photograph, the overall brightness trend would form a smooth, downward-sloping glow from start to end. The decay curve is that long-exposure photograph of the room's acoustic energy. Individual reflections (sparks) are noisy and random, but the overall energy trend (the glow) reveals the room's true decay rate.
Technical Definition
From Impulse Response to Decay Curve
The impulse response h(t) of a room is a time-domain signal containing the direct sound, early reflections, and reverberant tail. To obtain the decay curve:
Method 1: Squared Impulse Response (Historic)
Square the impulse response to get instantaneous sound energy: E(t) = h²(t). This is noisy because individual reflections cause sharp peaks and valleys. Multiple measurements must be averaged (ensemble averaging) to get a usable curve. This was the only practical method before digital signal processing.
Method 2: Schroeder Backward Integration (Modern Standard)
Proposed by Manfred Schroeder in 1965 and standardised in ISO 3382-2:2008 Annex B, this method integrates the squared impulse response backward from the end of the recording:
EDC(t) = 10 × log₁₀[ ∫(from t to ∞) h²(τ) dτ / ∫(from 0 to ∞) h²(τ) dτ ]
In practice, the upper limit is replaced by the end of the measured IR. The result is a smooth, monotonically decreasing curve that represents the average energy remaining at each time point. A single impulse response measurement produces a clean decay curve — no ensemble averaging needed.
Extracting RT60
Once the decay curve is generated, RT60 is determined by fitting a linear regression to a portion of the curve:
- T30: Fit a line from -5 dB to -35 dB on the decay curve (30 dB range), then double the resulting time to extrapolate to 60 dB. This is the standard method per ISO 3382-2 when the dynamic range of the measurement is limited.
- T20: Fit from -5 dB to -25 dB, then triple the time. Used when background noise limits the usable dynamic range.
- T60: Direct measurement of the 60 dB decay range. Rarely achievable in practice because background noise floors are typically only 40 to 50 dB below the initial level.
EDT (Early Decay Time)
EDT is measured from the first 10 dB of the decay curve (0 to -10 dB), then multiplied by 6 to extrapolate to 60 dB. EDT is more perceptually relevant than RT60 because listeners are most sensitive to the initial decay. In rooms with non-uniform absorption (e.g., concert halls with absorptive seats and reflective walls), EDT and RT60 can differ significantly.
Why It Matters for Design
The decay curve reveals problems that a single RT60 number hides. A "double-slope" decay — where the curve starts steep then becomes shallower — indicates coupled spaces: sound energy from an adjacent volume (a stage house, a balcony, a corridor) is feeding back into the main room and extending the tail. A wavy or irregular decay curve suggests flutter echoes or room modes that need targeted treatment.
Acoustic consultants examine decay curves at each octave band to understand frequency-dependent behaviour. A room might have a clean, straight decay at 1 kHz (well-treated mid-frequencies) but a long, curved tail at 125 Hz (insufficient bass trapping). The frequency-dependent decay curve is the diagnostic tool that tells you where treatment is needed.
How AcousPlan Uses This
AcousPlan's results dashboard shows the calculated energy decay curve for your room model at each octave band. When you import measured data, the platform generates the Schroeder-integrated decay curve and overlays it against the predicted curve, highlighting discrepancies between model and measurement. The T20 and T30 values are extracted from the curve and reported alongside the Sabine and Eyring RT60 predictions.
Related Concepts
- What is the Schroeder Method? — The integration technique for decay curves
- What is an Impulse Response? — The raw data behind decay curves
- What is RT60? — The parameter extracted from the curve
- How to Measure Room Acoustics — Full measurement workflow
- What is Clarity (C80/D50)? — Early energy metrics from the same data
Calculate Now
Visualise the decay curve for your room design. AcousPlan calculates and plots energy decay at every octave band so you can diagnose acoustic issues before construction.