Late Lateral Energy

The late lateral energy level, $L_J$, represents the relative level of late-arriving lateral sound energy compared to the reference response measured at 10 m distance in a free field. This parameter is evaluated from the impulse response obtained with a figure-of-eight pattern microphone, in combination with a calibrated omnidirectional sound source [1].

It can be calculated according to the following equation:

$$L_J = 10 \lg \left[ \frac{ \int_{0.080}^{\infty} p_L^2(t)\, dt } { \int_{0}^{\infty} p_{10}^2(t)\, dt } \right] \, \text{dB},$$

where the integration in the numerator starts at $t = 0.080 \,\text{s}$, corresponding to the onset of late-arriving sound.

The terms can be expressed as follows:

• $p_L(t)$: instantaneous sound pressure in the impulse response measured with a figure-of-eight pattern microphone;
• $p_{10}(t)$: instantaneous sound pressure in the impulse response measured with an omnidirectional microphone at a distance of 10 m in a free field;
• The excitation is provided by a calibrated omnidirectional sound source.

The figure-of-eight microphone is oriented so that its null points towards the stage source position (or average source direction). This ensures the microphone responds predominantly to lateral sound energy, while minimizing the contribution of the direct sound. In simulations, the figure-of-eight characteristic is approximated by deriving it from ambisonic signals through spatial receiver processing.

Thus, $L_J$ is an indicator of the strength of lateral reflections arriving after 80 ms, which are important for spatial impression and listener envelopment in concert halls.

Frequency-Averaged Late Lateral Energy Level

The frequency-averaged late lateral sound energy level, $L_{J,\mathrm{avg}}$, combines values across the four octave bands centered at 125 Hz, 250 Hz, 500 Hz, and 1000 Hz [1]. It is calculated as:

$$L_{J,\mathrm{avg}} = 10 \lg \left[ 0.25 \sum_{i=1}^{4} 10^{L_{J_i}/10} \right] \, \text{dB},$$

where:

• $L_{J_i}$ is the late lateral energy level in octave band $i$;
• $i$ corresponds to the octave bands with center frequencies 125 Hz, 250 Hz, 500 Hz, and 1000 Hz.

Late lateral sound energy is closely related to listener envelopment and the sense of spaciousness in auditoriums.

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References

[1] ISO 3382-1:2009 Acoustics — Measurement of room acoustic parameters — Part 1: Performance spaces.