Theoretical Considerations of Acoustics in Rooms – Energy Criteria and Spaciousness

As mentioned in the acoustic introduction to home theater, to create a home theater regardless of the shape and size of the space, we need to consider the best equipment with the best layout in space. To implement the above, we will explain the theoretical issues. We have already gone to the two sections of Room acoustic parameters and time criteria, and now we are going to discuss the topics of energy criteria and Spaciousness.

Energy Criteria

Clarity

Clarity deals with the balance between the early and late arriving energy and is defined as the ratio of the sound energy in the first 50 ms (speech) or 80 ms (music), and the rest of the energy received after the given initial time interval. As mentioned before the clarity becomes better with a greater contribution of the early reflections occurring within the first (50-80 ms) time interval.

Since this project deals with the acoustics in home theaters both time intervals are reasonable for calculations.

where t=50 for speech and t=80 for music

Spaciousness

Spaciousness is an important factor for the listener regarding the perception of auditory events. Spaciousness can be created by early lateral reflections from side walls, which gives the listener the feeling of being enveloped by the sound due to the impression of the sound arriving from different directions.

Apparent Source Width (ASW)

Apparent source width (ASW) is the perceived sound image, which is wider than the physical source. The source appears wider when there is a high level of early lateral reflections occurring within 80 ms of the arrival of the direct sound.

Listeners Envelopment (LEV)

LEV can be used to describe the feeling of being inside and surrounded by the reverberant sound field in a room and is improved by late lateral reflections (after 80 ms). Frequencies in a range from 100 to 1 kHz mostly contribute to the perception of LEV.

Lateral Energy Fraction (LEF)

The lateral energy fraction is an objective measure to compare the lateral sound energy with the energy from all directions. The subjective parameters ASW and LEV are both correlated with LEF. The lateral energy fraction can be given as:

where h1 is the impulse response of the lateral reflections and h is the impulse response of all the reflections.

Figure below depicts the frequency ranges over which several audible effects are dominating the perceived soundscape during sound reproduction in rooms.

Interaural Cross-Correlation Coefficient (IACC)

Lateral reflections can cause two different sound pressure levels at each of the listener’s ears. This can be measured and described through the interaural cross-correlation coefficient.

  • t1, t2 define the time interval of the impulse response.
  • 𝜏 [-1 ms, +1 ms] is the interval (roughly the time delay of sound between left and right ear) for finding the maximum of the correlation.
  • hL, hR are the impulse responses (octave band filtered) measured at the entrance of both ears.

  • IACC takes values between 0, for no correlation, and 1 for perfect correlation.

A final value can be obtained by alpha which increases with the decorrelation of the sound at each ear.

The IACC coincides with the impression of the Apparent Source Width for the time interval [0 ms, 100 ms] and corresponds for a later interval [100 ms, 1000ms] with the perception of being enveloped by the sound described through the LEV.

Speech Intelligibility

Speech intelligibility is a useful parameter to determine the audibility of speech e.g. reproduced by a center channel in home theaters, in a room. A common way to assess speech intelligibility is by measuring the speech transmission index STI, which determines the modulation transfer as the ratio between the transmitted and the received degree of modulation.

What has been said so far and what we will discuss in detail in the future, will pave the way for creating a home theater of the highest quality. The audio products offered in Saba Smart systems, which include Dali speakers, Yamaha amplifiers and inakustik cables with their great variety and high quality, make it possible to implement any type of equipment according to the relevant needs.

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