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 5-1 Part 1. Direct and Reverberant Field 1
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Do curso por Korea Advanced Institute of Science and Technology
Introduction to Acoustics (Part 2)
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WAVE PROPAGATION IN SPACE / DUCT ACOUSTICS
For the last, you will learn Helmholtz Resonator and the phenomenon about the duct acoustics
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Yang-Hann KimProfessor
Mechanical Engineering
Let's
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Let's think about what we learned in the
in the last lecture, for acoustically
large room or space, in general.
Oh, we expect that the sound pressure level
will decay, so
like
60B down per octave of length
And, and in this region we call this is direct field.
Because, the and there's no
reflection, therefore energy is decaying
as the, the as the observation,
is, is getting doubled.
And we will prove that anyway, and then some oscillation due to
reflection, from the wall.
And then at certain distance from the source we could imagine that.
Some space would provide constant sound pressure,
and that this field that we call diffuse sound field.
And including diffuse field up to here, we call reberveration sound field.
And of course this is the distance.
[SOUND]
Okay.
Especially for acoustically large space, Sabine's theory.
Says that the aa, rate of change of
reverberant sound field, with respect to time, he found it is proportional to
energy density of reverberant field
with respect to some characteristic time T, tau, and a minus.
And later on he found that the characteristic
time tau is related with 1 over open area window.
And then he found that this is actually 4 over C and V over As.
Then, having some derivation, we found that
the reverberation period, which is defined as the time required
to have energy decay 60 dB down
is related with interesting number 0.161, and the volume
of space and then divided by open area window.
Okay that's what we learned in the last lecture.
And our interest it would be.
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How far we can, I mean, if there is a room
if there is a sound source.
And depending on the position of listeners say, this is the distance R.
The sound energy he will be hear, would be sum of energy he will hear.
I say this is total sound energy,
could be e direct plus e reverb.
'Kay.
And then one could think that.
There is some distance, r0 that
can be regarded as a
distance where we can sufficiently
hear the direct sound. Okay.
This kind of, you know, the interesting
measure could be very valuable to evaluate
the, the quality of rooms acoustics.
Before we only evaluate the quality of a room assuming
that the sound field inside is diffuse field.
Okay, therefore, it doesn't matter where you are located.
But if we think little bit more carefully
that is too brave assumption, and we could think that depending on the position.
The effect of direct sound field compared
with the reverberant sound field will be different.
So we want to find out this kind of value.
That we call sometime characteristic
distance from the source.
In other words, there is some distance we can characterize the
quality of a sound that one can hear from the room.
I mean, in the room.
Okay, so if r0 is very
long, that means we are
hearing sound mostly direct sound
in the, in the large, I mean, r0.
If r0 is very small, then what you hear
would be, within small distance, what you hear would be mostly reverberant.
So that kind of you know, distance concept would be nice.
And then later on we will call this radius
of reverberation.
The first topic of today's lecture is to
introduce radius of reverberation, okay?
OKay, let me continue to
talk about this [SOUND] to get the result.
Okay, first in free
field or direct field.
We said in the graph,
SPL would decay 6 dB,
6 dB per octave, or
doubling the distance.
Okay, let's prove this.
Suppose, for simplicity,
I have monopole here, and
radiate sound, and say I measure
power at distance r1, and then I measure
sound at distance r2, and r2 is 2r1.
Okay.
Then I can say the power coming out from
this surface would be power coming out
from this surface would be intensity
at r equal r1 multiply by 4 Pi r1
square that is power out and r1.
That is quite straightforward.
And the power out at r2 would be
intensity at r2 multiplied by 4 pi r2 square.
Okay, right, so and,
we know that this power out
through the surface that is
made by the radius of r1.
As to be same as the power out.
Through the surface with radius of r2, because the fluid we are considering is,
does not have any element that, that observes sound energy.
In other words, the, the, the medium has no viscosity.
So only energy decay is due to so called spreading of some.
Therefore, therefore we
can write according to this
relation we can write
I_r1 4 pi r1 is equal to
I_r2 4 pi r2 square, right?
Therefore, therefore
again the intensity
ratio, between I_r2
and I_r1 is equal to
simply r1 divided by
r2 square.
And that is 1 over 4.
Right.
It's too simple?
Now, then, how much sound power is decreasing
in terms of log scale, and I can write like this,
that is ten log ten.
1 over 4, and this is minus 6 dB.
And it notes that the intensity is,
intensity is. the magnitude of intensity is P multiplied by velocity.
All right?
And the velocity for the case
of plane wave would be, what?
For plane wave, the impedance
is rho0 c therefore the velocity is P
over rho0 c so in this case we can say that is a P square
over rho0 c, right?
So the intensity ratio is the same as the ratio of SPL.
So we can say that SPL will reduce by 6 dB
as double the, the distance from the sound source.
Okay, that's good.
And also recall I mean this explains the, the 6 dB down in direct field
or free field when they use a direct
means direct, direct field the terminology emphasise that.
What we are hearing is only direct field, direct
sound from the source, nothing come from the reflection.
When we use the terminology free field, it emphasize that what we hear
is free from reflection, so actually it has the same meaning.
Okay, now this explains what's
happening in free field or dialect field.
But you do want to have a description that describes the reverberant field, o kay.
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