Derivation of Sabine's formula for reverberation time

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SUMMARY

The discussion focuses on the derivation of Sabine's formula for reverberation time, specifically addressing the relationship between acoustic energy decay and time. The key equation derived is tau_W = 4V/(cA), where tau_W represents the time constant for energy decay, V is the volume of the space, c is the speed of sound, and A is the total absorption area. T60 and T30 are defined as the times required for acoustic energy to decay by -60 dB and -30 dB, respectively, and are directly related to tau_W through multiplication by constants.

PREREQUISITES
  • Understanding of acoustic energy concepts
  • Familiarity with the speed of sound in various media
  • Knowledge of reverberation time definitions (T60, T30)
  • Basic grasp of exponential decay functions
NEXT STEPS
  • Study the mathematical derivation of Sabine's formula in acoustics
  • Explore the relationship between volume, absorption area, and reverberation time
  • Learn about alternative formulas for reverberation time, such as Eyring's formula
  • Investigate practical applications of reverberation time in architectural acoustics
USEFUL FOR

Acoustic engineers, physicists, architects, and anyone involved in sound design and room acoustics will benefit from reading this discussion.

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https://courses.physics.illinois.edu/phys406/Lecture_Notes/P406POM_Lecture_Notes/Derivation_of_the_Sabine_Equation.pdf
I can't understand anything from the above link.
Is there any alternative way to derive Sabine's formula. I searched in google but coundn't find anything.
 
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Hmmm, looks pretty clear to me, but it was obviously written by a physicist for physicists.

The first part is deriving that the time derivative dW/dt of the acoustic energy W is proportional to the acoustic energy.

From that it follows that the acoustic energy must decay exponentially, with the time constant derived above tau_W = 4V/(cA).

T60 (T30) is defined as the time by which the acoustic energy has decayed by -60 dB (-30 dB) = 10^-6 (10^-3).

tau_W is defined as the time by which the acoustic energy has decayed by 1/e. T60 and T30 are just tau_W multiplied by constants.
 

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