Sabine's Formula:

• Prof. Sabine observed the concept of reverberation time for varieties of conditions like empty room, furnished room, small room, auditorium. etc.
• He concluded the following:
  • Reverberation time depends upon reflectivity of sound from various surfaces available in side of the hall. If the reflection is good, reverberation time of the hall will be longer as sound takes more time to die out.
  • Reverberation time depends upon volume of the hall that is T$\alpha$ V.
  • Reverberation time depends upon coefficient of absorption of various surfaces present in the hall. For shorter reverberation, absorption should be more.
  • As absorption coefficient is found to be increased with increase in frequency, reverberation time decreases with frequency.
    Hence, Reverberation time T$\alpha \dfrac V A$
    where V: Volume of the hall.
    A: Absorption or T =$K \dfrac V A$
    where K: Proportionality constant.
• It has been further observed that is all the parameters are taken in SI then, proportionality constant is found to be 0.161.
  Hence, T = 0.161$\dfrac V A \cdots (1)$
• Hence Equation (1) is Sabine's formula.
• Absorption A given in equation (1) represents overall absorption which is given as:
  $A = \sum^n_{i=1} aS=a_1S_1+a_2S_2+....a_nS_n$