How Do You Calculate Reverberation Time and Sound Levels in an Auditorium?

  • Thread starter roldy
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In summary: It is important to have a lower reverberation time in order to have clear and understandable sound in an auditorium.
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roldy
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Homework Statement


The surfaces of an auditorium are 200ft x 50ft x 30ft and have an average absorptivity a=0.29.

(a) What is the reverberation time?
(b) What must be the power output of a source if it is to produce a steady-state sound pressure level of 65 dB reference 20 [tex]\mu[/tex]Pa?
(c)What average absorptivity would be required if a speaker having an acoustic output of 100 [tex]\mu[/tex]W is to produce a steady-state level of 65dB reference 20[tex]\mu[/tex]Pa?
(d) Calculate the resulting reverberation time, and comment on its influence on the intelligibility of the speaker


Homework Equations


Reverb time=0.191V/(Sa)
S=surface area
a is the average absorptivity coefficient
V is the volume of the room
A is the absorptivity

[tex]W=10^{\frac{SWL}{10}}*W_o[/tex]
W is the power output (Watts)
SWL is the sound power level
[tex]W_o=10^{-12}[/tex]

[tex]SIL=10^{-12}*10^{\frac{SPL}{10}}[/tex]
SIL=sound intensity level
SPL=sound pressure level

[tex]SWL=SIL-10log\left(\frac{4}{A}\right)[/tex]

a=A/S

[tex]W=10^{\frac{SWL}{10}}*W_o[/tex]

The Attempt at a Solution



(a)S=2(50*30)+2(200*30)+2(200*50)=35000

Reverb time=[tex]\frac{0.101*200*50*30}{35000*.29}=4.759[/tex]sec


(b)First I found A
A=a*S=0.29*35000=1015

Then I found SIL from the SPL given

SIL=[tex]10^{-12}*10^{\frac{65}{10}}=3.16*10^{-6}W/m^2[/tex]

Then I found the SWL.

[tex]SWL=SIL-10log\left(\frac{4}{A}\right)=3.16*10^{-6}-10log\left(\frac{4}{1015}\right)=24 W/m^2[/tex]

Then I calculated the power out put from [tex]W=10^{\frac{SWL}{10}}*W_o[/tex]

W=[tex]2.51*10^{-10}[/tex] Watts

Did I do this right? This seems like a really small number for this situation

(c) I just solved [tex]SWL=SIL-10log\left(\frac{4}{A}\right)[/tex] in terms of A

[tex]A=\frac{4}{10^{\frac{SIL-SWL}{10}}}=4*10^9 m^2[/tex]

So then the average absorptivity is [tex]a=\frac{4*10^9}{35000}=1.14*10^6[/tex]

Now this doesn't seem right if I think about it logically. If my power is really small (part b), why would I need a tremendous amount of absorptivity? I can solve part d easily but if I solved either part b or c then d will be wrong. Can anyone see if I made a mistake if any?
 
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  • #2
(d)Reverb time=\frac{0.101*200*50*30}{35000*1.14*10^6}=4.2secThis reverberation time is on the higher end and will significantly reduce the intelligibility of the speaker.
 

FAQ: How Do You Calculate Reverberation Time and Sound Levels in an Auditorium?

What is reverberation?

Reverberation refers to the persistence of a sound in an enclosed space after the original sound source has stopped, caused by multiple reflections of sound waves off the surfaces of the room.

What factors affect reverberation?

The size and shape of the room, as well as the materials and furnishings within it, can affect reverberation. Sound-absorbing materials, such as curtains or carpets, can decrease reverberation, while hard surfaces like concrete or tile can increase it.

What are some common applications of reverberation?

Reverberation is often used in music production to add depth and richness to recordings. It is also important in architectural acoustics, as it can affect the sound quality in performance spaces like concert halls or theaters.

How is reverberation measured?

The amount of time it takes for a sound to decrease in intensity by 60 decibels after the sound source has stopped is known as the reverberation time. This can be measured using specialized equipment, such as a sound level meter.

Can reverberation be controlled or manipulated?

Yes, reverberation can be controlled through the use of acoustic treatments, such as sound-absorbing panels or diffusers. It can also be manipulated in post-production through the use of digital audio effects.

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