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Acoustics Reverberation

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What is Reverberation? Reverberation is multiple, random, blended repetitions of a sound. Three parts: Direct Sound, Early Reflections, & Later Reflections. Reverberation Time (Decay Time) is the time required for the sound in a room to decay 60 dB (also known as RT60). This represents a change in sound intensity or power of 1 million (10 log 1,000,000 = 60 dB, or a change in sound pressure level of 1,000 (20 log 1,000 = 60 dB).

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Growth & Decay of Sound W. C. Sabine, the Harvard pioneer in acoustics introduced the concept of RT60.

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**Measuring Reverberation Time**

A common approach to measuring reverberation time. Figure B is a more common occurrence than figure A.

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**Measuring Reverberation Time**

The sound sources used to excite the room must have enough energy throughout the spectrum to ensure decays sufficiently above the noise to give the required accuracy. Both impulse sources and those giving a steady-state output are used.

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Impulse Sources Common impulse sources are balloon pops and starter pistols. The diagram shows the reverb decays at several different octave ranges using a starter pistol.

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Steady-State Sources Bands of random noise give a steady and dependable indication of the average acoustical effects taking place. Octave and 1/3 octave bands of random noise (white or pink) are most commonly used.

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Mode Decay Variations The fluctuations in the decays result from beats between closely spaced modes. The differences in the four decays is due to the random nature of the noise. It is good practice to record several decays for each octave for each mic position of a room. Acoustical flaws can often be identified from aberrant decay shapes.

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Room Modes When sound is emitted in a room with parallel opposing walls, the room exhibits a resonance at a specific frequency determined by the equation f0 = 1,130/2L (or 565/L), where L is the length (in feet) of space between the two walls. A similar resonance occurs at 2f0, 3f0, 4f0, etc. These resonances are called modes; specifically, axial modes.

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Frequency Beats 500 Hz 500 & 505 Hz 505 Hz

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**Modal Interaction with Decay**

The diagram shows four different axial mode frequencies in the octave centered on 63 Hz. The lower the frequency, the less axial modes there are, so the more noticeable the beats become.

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Types of Room Modes Axial modes are derived from two walls, tangential modes are derived from four walls, and oblique modes are derived from all six surfaces.

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Frequency Effect This diagram shows typical fluctuation due to modal interference.

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**Variation with Mic Position**

There is enough variation of reverb time from one position to another in most rooms to justify taking measurements at several positions. The average gives a better statistical picture of the behavior of the sound field in the room. If the room is symmetrical, measure only one side to minimize time and effort.

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Acoustical Coupling Acoustically coupled spaces are quite common in large public gathering spaces, but are also found in offices, homes, and other smaller spaces. Assuming that slope A is correct for the main room, persons subjected to slope B would hear inferior sound.

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**Electroacoustical Coupling**

What is the overall effect when sound picked up from a studio having one reverberation time is reproduced in a listening room having a different reverberation time? The combined reverb time is greater than either alone If the reverb time of each room alone is the same, the combined reverb time is 20.8% longer than one of them.

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**Optimum Reverberation Time**

The best reverb time for a space in which music is played depends on the size of the space and the type of music. Spaces for speech require shorter reverb times than for music.

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**Optimum Reverb Time Examples**

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**Optimum Reverb Time Examples**

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Bass Rise Taking the 1 kHz value as a reference, rises of 80% at 63 Hz and 20% at 125 Hz were found to be acceptable in studios designed for voice recording.

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**Living Room Reverb Times**

The average reverb time decreases from 0.69 seconds at 125 Hz to 0.4 seconds at 8 kHz.

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The Sabine Equation The absorption coefficients published by materials manufacturers are typically Sabine coefficients and can be applied directly in the Sabine equation.

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**Absorption and Absorption Coefficients**

Absorption: in acoustics, the conversion of sound energy to heat. Absorption Coefficient: the fraction of sound energy that is absorbed at any surface. It has a value between 0 and 1 and varies with the frequency and angle of incidence of the sound. Multiplying the surface area (in sq. ft.) by the absorption coefficient results in absorption units (sabins).

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**Reverberation Calculations**

The diagram shows an example of the RT60 calculations using the Sabine equation.

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**Reverb Time (RT60) Calculations**

1) Calculate the total areas of each type of surface 2) Find the absorption coefficients for each type of surface for the six frequencies: 125 Hz, 250 Hz, 500 Hz, 1 kHz, 2 kHz, & 4 kHz 3) Multiply the area by the coefficient to determine the absorption units (sabins) 4) Add all sabins to find total sabins for each frequency 5) Plug all info into the Sabine equation to find the reverb time (RT60) for the room.

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**Determining Room Treatments**

The result of the RT60 calculations show a short reverb time at low frequencies, long reverb time in the midrange, and medium reverb time in the high frequencies.

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**Determining Room Treatments**

1) Find treatments that will achieve the desired response 2) Determine how much treatment (in sq. ft.) would be necessary to add the desired amount of absorption (sabins) by dividing the sabins by the absorption coefficient. The result will be the amount of treatment in sq. ft.

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