Learners might have learned the basic concepts of the acoustics from the ‘Introduction to Acoustics (Part 1).’ Now it is time to apply to the real situation and develop their own acoustical application. Learners will analyze the radiation, scattering, and diffraction phenomenon with the Kirchhoff –Helmholtz Equation. Then learners will design their own reverberation room or ducts that fulfill the condition they have set up.
Lecture 4-2 Part 1. Sabine's Theorem 1
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From the course by Korea Advanced Institute of Science and Technology
Introduction to Acoustics (Part 2)
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From the lesson
REVERBERATION PERIOD AND ITS DESIGN APPLICATION
Now you will learn very practical acoustical phenomenon. With reverberation period and Sabine's theorem, you will be able to design an acoustical room that satisfies given condition.
Meet the Instructors
Yang-Hann KimProfessor
Mechanical Engineering
Today, we will talk about Sabine's Theorem.
That has to do with the acoustically very large room.
Sabine said the very large room can be
characterized by the reverberation time or period,
which is related with size of room and open area window.
Where and in the last lecture,
we found that the reverberation period of
this room was estimated by myself very roughly.
And then, we got about 0.9 second.
But our measurement system is very expensive.
Estimate reverberation period, 0.7 second.
Okay. And if you look at
the reverberation period of various famous room,
you can find that interesting number.
For example, the whole famous Vienna Symphony Hall,
that has a volume of
15,000 and reverberation unoccupied
is about three second.
Okay, so, the Vienna Hall reverberation period when it is occupied,
two second, unoccupied, three second.
And Birmingham Symphony Hall reverberation period
is about 2.5 and it is not occupy,
but if it is occupy,
it is about two second.
And Boston Symphony Hall is about 1.9 second when it is occupied.
When it is not occupied, it is 2.5.
Dallas case, 2.9 and 2.8. Stuff like that.
So, what you can see here,
the reverberation period of most of the Symphony hall is
ranging somewhat in 2.52 second.
So, it is more than we expected, okay?
If you go to the very old Catholic,
Cathedral, things like that,
it is more than sometimes three seconds.
So, you feel very revolved around a soundfield.
And this table was adapted from Beranek Concert Halls and Opera Houses,
which is published in 2004.
Okay. Now, in some cases,
most cases I believe,
we would like to increase reverberation period in most cases.
And then, we have to select the area that we wanted change, okay?
Can you move up this?
Then, what we have to do is for example,
in this hall, we have Alpha 181,
maybe I say, this is the ceiling.
And Alpha 282, this is the area on the back side, and Alpha three,
A3, which would be the area covered by you guys and then,
Alpha four, A4, which would be at the bottom, things like that.
And then, we have to decide which one will effectively
reduce or increase the reverberation period, okay?
So, if I rewrite this again,
reverberation period is actually
easiest to get is to increase the volume, okay?
But this case, it costs a lot.
So, Alpha one A1,
and Alpha two A2,
plus Alpha four A4.
In trial and error.,
you could say, okay.
If I reduce R power four,
then how much reverberation period it would be increased?
And also, note that,
this reverberation period is also function
of frequency or wavelets, right?
As you can easily anticipate,
the reverberation period will increase as wavelengths decrease.
Okay. And also, note that the absorption coefficient is
also functional frequency normally even if we have a same of or whatever,
the absorption coefficient is also
functional frequency and it will increase as frequency increase.
So, what you measure over here using the instrument,
is the reverberation average in sense.
Okay. But sometimes as an architecture acoustician,
you may want to increase
the reverberation period at certain frequency or certain frequency band.
All right? Also, this equation says there are some way to,
this equation indicates that we can
measure absorption coefficient Alpha using reverberation period.
Then, what is Alpha?
Absorption coefficient?
Well, definition of
absorption coefficient is actually measuring or indicating
how much energy is observed by the observing material.
So, that is the ratio between.
So, this is the energy of instant sound and this is the energy of reflected sound.
So, this term is the energy which is observed at certain frequency.
Okay. We would like to measure it using reverberation period.
How to do it. Okay.
First, we have to make diffuse field, right?
So, how to make a diffuse field.
You need to have
the sound field that has to be
uniform irrespectable to the position where you measure the sound.
So, the reflection has to be very random.
Therefore, usually to measure diffuse field,
you need to have some box that has different size.
Okay? Which sometimes will called reverberation chamber.
And we measure reverberation period when there
is nothing over there, okay?
Then, from this formula we can say,
we measure reverberation period empty,
meaning that there is no sound absorbing material.
That is 0.161V divide by A0.
So A0 is the total area.
Then you put some sound absorbing material over here.
Then you measure it with a specimen.
That is, I can write, with a specimen.
So our objective is to measure this.
So, we can re-measure this,
then we can measure this.
And absorption quotient alpha, multiplied by S,
the S is the area of
specimen is equal to
the A0 minus A specimen.
Not the other way around.
A specimen minus A0.
Yeah. If you add this one over there,
that is what we measure, right?
Of course there is some little difference in the area.
Yeah. Maybe if you want to take
out what could be absorbed by this area,
but this is approximately true.
So therefore, we can measure alpha,
that is the absorption quotient of the specimen
by A specimen minus A,
open area window, divide by S. Therefore,
from the equation over there,
we can write Aspecimen,
let say in short Asp that is equal to 0.161,
we divide by T60 specimen,
and A0 is point 0.161,
we divide by T60 empty.
Therefore, the alpha is equal to 1.161V
divide by S,
one over T60 specimen minus one over T60 empty.
And then you can measure alpha for
any frequency you have interest, okay?
Well, this imaginable system
requires big reverberation chamber.
If you don't have that kind of chamber,
you need to find out some alternative measurement way.
An alternative away to measure the absorption quotient.
Okay. What would be the alternative way?
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