Auditorium Acoustics

During the Easter holidays, my family and I watched a stand-up comedy show in the London Palladium. With this C3 project in mind, we snapped a few photographs to lead me to explore the physics behind sound and its projection in auditoriums.

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The chief issue sound engineers must solve when building a theatre is to ensure the entire audience can hear the performer. The London Palladium has a capacity of 2,286, and hearing Katherine Ryan wasn’t an issue for many, if any, at her show. The engineers achieved this in two ways. Of course, with the use of a microphone and multiple overhead speakers (one seen in the top photo), but also with the shape of theatre. This is key for many operas and plays, in which singers and directors may reject the use of speakers. The London Palladium has three tiers of seating, and boxes to the side. This distributes the large audience vertically, shortening the distance between the stage and the backrow. With this, direct sound waves have less time to lose intensity, and the entire audience obtains a sufficient volume.

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It is these direct sound waves which engineers want to enhance, as indirect sound waves, reaching audience members after being reflected off a surface(s), contribute to interference. As reflected sound waves travel longer than direct sound waves, they are most likely not in-phase with each other or with the direct sound waves; hence, when these waves’ paths cross, they superpose and may interfere, distorting the original sound wave, resulting in lost clarity.

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These problems are amplified in “shoebox” rooms, as sound waves can bounce from side to side, off two smooth, flat walls opposite each other. This can cause an effect called a flutter echo. To solve this, the architecture and interior design come into play, as curved walls and irregular geometry on the walls is utilised. Nevertheless, sound waves can still be reflected and cause interference.

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To further reduce the possibility and impact of interference, sound engineers generally aim to reduce the reverberation time of sound in the auditorium. This is calculated using Sabine’s Equation: RT60=(0.161V)/(Sα), where V is the room’s volume (in m3), S is the room’s surface area (in m2), α is the absorption coefficient (ranging from 0, fully reflective, to 1, fully absorptive), and RT60 is the reverberation time, the time it takes for sound to decay by 60 decibels after the source stops emitting the sound (in s). For theatre involving speech and music together, an RT60 between 1.5 and 2.5 seconds is ideal. For speech alone, an RT60 of about 1 seconds is better, letting articulation of speech be clear, while for music, depending on the instruments used, an RT60 even above 3.5 seconds may be used, to enhance the richness of the sound. If the RT60 is too high, the room is considered echoic, as the sound waves reflect and interfere with each other for too long and too much. If the RT60 is too low, the room is considered acoustically dead.

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As engineers aim to reach ideal reverberation times in an auditorium or hall, assuming it has already been built and the space’s volume or surface area cannot be significantly altered, they change the absorption coefficient by utilising different materials, and seating arrangements. With all other variables constant, a denser crowd absorbs more, and the more upholstered a seat is, the more it absorbs, reducing the reverberation time, and increasing clarity of sound. (As seen in table 6.3 of Heinrich Kuttrud’s book, “room acoustics.”)

Similarly, softer materials may be used on walls, with foam having a higher absorption coefficient than brick walls. (As seen in table 9.1 of Heinrich Kuttrud’s book, “room acoustics.”) 

Another goal of sound engineers when designing a theatre is to ensure the entire audience has a similar experience; so, they must ensure that sound spreads evenly to prevent “hot spots”, where many sound waves focus resulting in interference, or “dead zones”, where few waves reach, making the sound dull and faded. To deal with this, engineers will employ a hybrid approach involving purpose-built absorbers and diffusers in relation to the sometimes speakers. A diffuser is built to reflect sound waves off its irregular surface, to scatter the sound in different directions. Thus, they are generally placed on ceilings of auditoriums to reach all members of the crowd. These are most vital concerts venues, where the musician and audience care more about experiencing the richness of the sound. Meanwhile, rear walls are generally padded with absorptive materials, reduce the sound waves reflecting across back through the venue.

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Overall, acoustics is a vital part of designing and constructing auditoriums, with engineers having to take the physics behind sound waves into account. This is highlighted by the error in constructing the Royal Albert Hall; the dome-shaped ceiling meant that there was a concave, reflective surface for all sound to bounce and echo off of, resulting in a running joke about hearing every piece of music playing the Royal Albert Hall twice, and so requiring a redevelopment with 135 mushrooms (a form of acoustic diffusers) being hung. This was also a miscalculation though, and 50 of the mushrooms had to be removed afterwards.

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Sources

Sabine, W. C. (1922a). COLLECTED PAPERS ON ACOUSTICS [Book]. HARVARD UNIVERSITY PRESS. https://ia601607.us.archive.org/4/items/collectedpaperso00sabi/collectedpaperso00sabi.pdf

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Kuttruff, H. & Institut für Technische Akustik, Technische Hochschule Aachen. (2000). Room Acoustics (Fourth edition). Spon Press. https://danylastchild07.wordpress.com/wp-content/uploads/2016/05/room-acoustics-kuttruff.pdf

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LONG, M. (2006). Architectural  Acoustics. Elsevier Academic Press. https://archive.org/details/ArchitecturalAcoustics_201901/page/n3/mode/2up

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Larson Davis. (n.d.-b). Reverberation time in room acoustics. https://www.larsondavis.com/learn/building-acoustics/Reverberation-Time-in-Room-Acoustics#:~:text=RT60%20%3C%201%20s:%20Good%20for,for%20both%20speaking%20and%20music.

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Fiona. (2023, October 20). Understanding Acoustics in Theater Auditorium - Leadcom Seating. Leadcom Seating.

https://www.leadcomseating.com/blog/sound-spaces-understanding-acoustics-theater-auditorium/

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Acoustic Geometry. (2013, August 1). How sound works (In rooms) [Video]. YouTube. https://www.youtube.com/watch?v=JPYt10zrclQ

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Cox, T. J., D’Antonio, P., University of Salford, & RPG Diffusor Systems Inc. (2004). Acoustic absorbers and diffusers. Spon Press. https://www.eBookstore.tandf.co.uk