WEBVTT
Kind: captions
Language: en
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.
So,
00:00:15.219 --> 00:00:22.270
welcome to the NPTEL lecture on Architectural
Acoustics the 5th lecture today. The fifth
00:00:22.270 --> 00:00:29.070
lecture is all about the Near and Far Field
Propagation and Loudness. And this fifth lecture
00:00:29.070 --> 00:00:34.480
is the last lecture of our first week course
and you will go to the some other topic
00:00:34.480 --> 00:00:40.339
in the second week. And the the architectural
physics the architectural in the building
00:00:40.339 --> 00:00:45.499
physics is going to be end with this lecture.
So, if you remember in the last lecture what
00:00:45.499 --> 00:00:51.809
we discussed is the sound pressure level,
sound intensity level, and how they can be
00:00:51.809 --> 00:00:59.030
added and what is the way? . The particular
conversion from the level to the the intensity
00:00:59.030 --> 00:01:04.049
or from the intensity to the level is going
to concern I am going to happen.
00:01:04.049 --> 00:01:09.570
So, in this lecture lecture number 5 again
I have to learning objective, the first
00:01:09.570 --> 00:01:16.660
1 is you have to differentiate the near
and far field propagation of the sound by
00:01:16.660 --> 00:01:23.280
this lecture can you differentiate I mean
after the this lecture, if you are going
00:01:23.280 --> 00:01:26.040
through properly you must differentiate between
that.
00:01:26.040 --> 00:01:32.610
And, then you must correlate between the
frequency sound level and this loudness of
00:01:32.610 --> 00:01:37.490
the sound . And, that will be the main major
focus to this particular lecture .
00:01:37.490 --> 00:01:44.750
So, let us go to the sound intensity once
more in a different way . What is intensity?
00:01:44.750 --> 00:01:50.980
Intensity is nothing, but the power per unit
area. So, I can write like the power by area
00:01:50.980 --> 00:01:57.590
is equal to the intensity. And, if the power
is now further converted to the energy part
00:01:57.590 --> 00:02:02.000
time, because the energy per time is your
joule per second, which is your watt which
00:02:02.000 --> 00:02:07.030
is your power and power per area that is watt
per meter square is your intensity .
00:02:07.030 --> 00:02:16.410
Now, this area can be rewrite as the length
by volume. Now, further if I see this total
00:02:16.410 --> 00:02:23.440
things can be rewrite like this volume can
be taken into the below this. So, the energy
00:02:23.440 --> 00:02:29.730
by volume into length by time and length by
time is nothing, but the velocity of the wave
00:02:29.730 --> 00:02:33.200
.
So, let us now see how this conversion
00:02:33.200 --> 00:02:39.390
of the energy and volume can be done. As,
we know that the energy is nothing, but the
00:02:39.390 --> 00:02:44.440
kinetic energy of the particles, which is
under the motion . So, it is half into mass
00:02:44.440 --> 00:02:50.650
into V max square, because the velocity of
the particle also we will fluctuate and
00:02:50.650 --> 00:02:55.959
it is minima and there is a maxima.
So, the the maximum velocity of the particle
00:02:55.959 --> 00:03:03.110
is A into omegas omega and the this is square
of that and the the the volume of mass in
00:03:03.110 --> 00:03:08.090
into density.
So, if this 2 are added together in this particular
00:03:08.090 --> 00:03:17.640
form, then the intensity can be rewrite as
half into m A omega square into rho by m because
00:03:17.640 --> 00:03:24.620
it is volume now and into cc is the the the
wave velocity. So, the intensity can be written
00:03:24.620 --> 00:03:31.140
in this form. So, you see this is very interesting
formula and you see the intensity of sound
00:03:31.140 --> 00:03:37.230
is depend upon the velocity, is depend upon
the rho density of the the media, it is depend
00:03:37.230 --> 00:03:42.530
upon the amplitude of the motion amplitude
of the propagation and also it is depend upon
00:03:42.530 --> 00:03:49.970
the frequency or the the angular the velocity
omega and this 2 are in square term.
00:03:49.970 --> 00:03:54.930
So, if I know the frequency, if I know the
amplitude and velocity of the sound and the
00:03:54.930 --> 00:04:00.980
density of the media, I can actually find
out what is the sound intensity . Now, go
00:04:00.980 --> 00:04:07.670
further head.
So, this intensity is again rewrite as the
00:04:07.670 --> 00:04:15.239
same equation can be rewrite as this rho c
A omega square by rho c, because the I have
00:04:15.239 --> 00:04:22.710
taken another rho c in the here and the and
dividing that by the numerator. And, here
00:04:22.710 --> 00:04:30.290
that I can get 2 such product and 2 such parameter
separately, and I can write is half into rho
00:04:30.290 --> 00:04:38.770
P square P 0 square and Z, what is this
2? The P 0 or the P 0 is the pressure amplitude
00:04:38.770 --> 00:04:46.040
of the wave propagation, which is nothing,
but your rho c A and omega and this is Z is
00:04:46.040 --> 00:04:52.169
called acoustical impedance which is the product
of the medium density rho and the wave velocity
00:04:52.169 --> 00:04:55.211
.
Now, why it is wave this pressure? So, let
00:04:55.211 --> 00:05:02.690
us find out from the the the units of them
rho is kg per meters cube, and the c is meter
00:05:02.690 --> 00:05:08.900
per second velocity amplitude is meter and
this is radian per second is the omega. So,
00:05:08.900 --> 00:05:16.650
if you just finally, come into that I mean
if you just finally, rewrite those things
00:05:16.650 --> 00:05:23.150
and rearrange the the units finally, you can
come down to the the Mpa, the mega Pascal
00:05:23.150 --> 00:05:29.120
the mega Pascal is nothing, but your pressure.
So, you can see from this particular equation
00:05:29.120 --> 00:05:39.250
that the I the intensity is proportional to
square of the pressure and that is why if
00:05:39.250 --> 00:05:45.900
you remember in the last lecture lecture number
4, we have discussed that the pressure
00:05:45.900 --> 00:05:50.760
square are the the intensity is proportional
to pressure square. And, that is why if the
00:05:50.760 --> 00:05:58.370
if you convert the pressure level to the decibel
level, you have to multiply that by virtue
00:05:58.370 --> 00:06:02.900
of 20 not 10.
And, if you convert the intensity to the intensity,
00:06:02.900 --> 00:06:08.860
level you have to multiply that by 10 and
if it, because it is logarithmic .
00:06:08.860 --> 00:06:17.790
So, next slide in this slide we will see the
the how the propagation of the sound is occur.
00:06:17.790 --> 00:06:23.461
The propagation of sound is spherical; it
is from a point source and it is going in
00:06:23.461 --> 00:06:30.340
a spherical way. So, in a in a air or in a
space it is going in a spherical way . So,
00:06:30.340 --> 00:06:35.290
from this particular point s source is going
in 3 dimension in this spherical way.
00:06:35.290 --> 00:06:42.680
So, the intensity is the what output divided
by the surface area of the sphere and as in
00:06:42.680 --> 00:06:49.050
when you go move further further from the
source to the sum further distance, your radius
00:06:49.050 --> 00:06:56.380
of the the distance is assume as a radius
your total sphere, that is going to increased,
00:06:56.380 --> 00:07:02.419
your surface area of the sphere is going to
increased and your total intensity is going
00:07:02.419 --> 00:07:05.500
to decrease.
So, if you are very near to the source the
00:07:05.500 --> 00:07:11.170
density is very high, because of sphere the
area of sphere is very small, if you go higher
00:07:11.170 --> 00:07:18.300
distance larger distance further more from
the source or so, your sphere is bigger, your
00:07:18.300 --> 00:07:23.630
radius is bigger, your surface area of the
sphere is bigger, your intensity is go
00:07:23.630 --> 00:07:29.160
going down and you hear less amount of sound
in the level point of view .
00:07:29.160 --> 00:07:37.729
So, the intensity is can be written as W w
is the output watt by 4 pi R square as you
00:07:37.729 --> 00:07:43.650
know the 4 pi R square is the surface are
of a sphere . Let us see small problem
00:07:43.650 --> 00:07:49.759
suppose this is a sound source of
sound as and it is giving a sound output as
00:07:49.759 --> 00:07:56.420
0.005 very very small wattage . And, you
are standing at the receiver is standing over
00:07:56.420 --> 00:08:01.890
here which is 7 meter away . And, if it is
so, I will find out what is the the surface
00:08:01.890 --> 00:08:06.160
area of a sphere, which is having 7 meter
of radius.
00:08:06.160 --> 00:08:14.780
So, that is why I am finding out the intensity
as this W by 4 pi R square and this is
00:08:14.780 --> 00:08:21.500
like this and finally, it is 8.12 into 10
to the power minus 7 watt per meter square.
00:08:21.500 --> 00:08:28.600
And, as and when you got this intensity, which
you are actually experiencing here at a distance
00:08:28.600 --> 00:08:37.330
7 meter by virtue of a sound output of 0.005
here, it is easy to convert these to the sound
00:08:37.330 --> 00:08:45.610
level . In that very old formula the 10 log
I by I reference is now your your here and
00:08:45.610 --> 00:08:51.800
your listening 59 dB sound .
Let us see the this particular problem or
00:08:51.800 --> 00:08:56.380
another problem in a different way. Suppose
this is a sound source and your with a dB
00:08:56.380 --> 00:09:03.029
meter at point a your at c bar act A of the
that sound and your receiving eighty dB at
00:09:03.029 --> 00:09:09.100
A. The sound pressure sound pressure level
at A or is 80 dB or the sound intensity level
00:09:09.100 --> 00:09:14.670
is eighty dB at A distance 3 meter.
The my question is what will this particular
00:09:14.670 --> 00:09:21.230
person get which is who is standing in B?
What will be the SPL or the SIL at B? Who
00:09:21.230 --> 00:09:27.470
that is B is 12 meter from the sound
source. I have I am going assume it is the
00:09:27.470 --> 00:09:33.670
spherical propagation it is the point source.
So, first find out what is the SPL is 80 dB.
00:09:33.670 --> 00:09:39.029
So, first try to find out the what will be
the intensity at this particular level by
00:09:39.029 --> 00:09:42.980
virtue of this formula .
So, by this it is 10 to the power minus 4,
00:09:42.980 --> 00:09:49.750
with the intensity at here . If this is
10 to the power minus 4 watt per meter square,
00:09:49.750 --> 00:09:56.230
which is on this particular sphere of radius
of 3, then what is the wattage of the sound
00:09:56.230 --> 00:10:03.209
output at the source? Which I can find out
from this equation because W by 4 pi 3 square
00:10:03.209 --> 00:10:09.380
is equal to this 10 to the power minus 4,
and solving this I can get the watt output
00:10:09.380 --> 00:10:16.649
or the power output of this particular source
is 0.0113 1. And if this is the wattage or
00:10:16.649 --> 00:10:22.190
the output wattage at the source, what could
be the intensity at the B, which is at at
00:10:22.190 --> 00:10:28.550
A distance of 12 meter 12 meter mix sphere.
So, that I can find out this W is now this
00:10:28.550 --> 00:10:34.370
and this 4 pi 12 square and this is the intensity
level. We can compare the intensity is now
00:10:34.370 --> 00:10:39.180
very very low with compare to the intensity
as A. So, I am expecting something less than
00:10:39.180 --> 00:10:47.101
80 dB over here of definitely and as I got
this intensity B I B, it is very easy to find
00:10:47.101 --> 00:10:55.490
out this particular level as your this old
formula by log this by I reference at 68 dB
00:10:55.490 --> 00:10:59.640
.
So, this particular problem gives you how
00:10:59.640 --> 00:11:07.760
from intensity level to thus taking consideration
of the spherical wave front propagation, how
00:11:07.760 --> 00:11:15.830
to find out the, what output? And from what
output to again a intensity in some different
00:11:15.830 --> 00:11:22.850
distance and from that you convert that intensity
to a intensity level or the sphere .
00:11:22.850 --> 00:11:31.320
So, the sound output from a suppose a source
is W is s and it at a distance R 1, which
00:11:31.320 --> 00:11:39.680
is nearer is the intensity is this and the
SPL is suppose just I 1 by I reference. Now,
00:11:39.680 --> 00:11:47.920
you go further further distance R 2,
which is higher than R 1 and definitely you
00:11:47.920 --> 00:11:55.450
will be experiencing less amount of intensity,
because the sphere is larger area is larger
00:11:55.450 --> 00:12:03.390
and your SPL 2 is your this.
And, then let us see this is going to be happened
00:12:03.390 --> 00:12:09.630
because your if your near to the source the
intensity is high, your decibel is high SPL
00:12:09.630 --> 00:12:14.310
1 will be higher than the SPL 2 . So, what
is the difference between them I am going
00:12:14.310 --> 00:12:22.850
to find out? So, difference is SPL 1 is this
SPL 2 is this and if you just operate this
00:12:22.850 --> 00:12:33.290
mathematical operation is 10 log A by B.
So, I 1 by I reference by I 2 by I reference.
00:12:33.290 --> 00:12:41.269
So, we can get it like this I reference get
cancelled. So, finally, I got 10 log I 1 by
00:12:41.269 --> 00:12:53.630
I 2 and now you replace the I 1 and I 2 from
here and got SPL 1 minus SPL to the difference
00:12:53.630 --> 00:13:00.260
between this 2 is R 2 by R 1 squares this
2 goes here.
00:13:00.260 --> 00:13:08.870
So, 20 log R 2 by R 1 and suppose if R 2 equal
to twice of R 1, if the distance is doubled,
00:13:08.870 --> 00:13:18.329
R 2 and this ratio is 2 log 2 is 3 I am sorry
log 2 is 0.3 0.3 into 26 dB .
00:13:18.329 --> 00:13:24.760
So, in case of a spherical propagation, if
the distance is double your decibel level
00:13:24.760 --> 00:13:32.920
is going to drop by 6 Db. This is the final
outcome of this particular the slide . Now,
00:13:32.920 --> 00:13:37.600
spherical propagation and cylindrical propagation.
Suppose, this is the unit source and it is
00:13:37.600 --> 00:13:43.639
give me a spherical propagation and the examples
of the spherical propagations are the some
00:13:43.639 --> 00:13:48.440
loudspeakers some human voice, some noise
from and small car or something like that,
00:13:48.440 --> 00:13:54.880
but if suppose there are so, many point multiple
point source in a very congested line or may
00:13:54.880 --> 00:14:00.930
be very close less are distance, linear
format.
00:14:00.930 --> 00:14:07.490
So, then you can superimpose those are the
sphericals and it will you will get a the
00:14:07.490 --> 00:14:13.779
cylindrical propagation. So, the watt
are the the examples of that may be a noise
00:14:13.779 --> 00:14:20.029
from a moving rail, maybe a traffic noise,
where there are lot of cars moving 1 after
00:14:20.029 --> 00:14:25.339
another which is the point source, but very
closely separated point sources in a road
00:14:25.339 --> 00:14:32.870
or may be a array of loudspeaker in any
theatre or any may be any any public address
00:14:32.870 --> 00:14:39.209
gathering field.
So, those are the the cylindrical propagation
00:14:39.209 --> 00:14:43.490
example of the cylindrical propagation. So,
we can actually say it is not as point it
00:14:43.490 --> 00:14:49.339
is a cylinder.
So, in case of a cylindrical propagation we
00:14:49.339 --> 00:14:55.459
will see the the propagation is from a cylinder
not from a point source so; that means, it
00:14:55.459 --> 00:15:00.639
is a line source. So, the length of the line
or the length of the source is L and by virtue
00:15:00.639 --> 00:15:06.630
of it has in having a radius, because if you
go further away from that line L your radius
00:15:06.630 --> 00:15:09.980
is increasing your surface area of the cylinder
is increasing.
00:15:09.980 --> 00:15:16.220
So, there I will take the same principal I
will what output that is the the power output,
00:15:16.220 --> 00:15:21.100
I have to divide that by the surface area
of the cylinder. And surface area of the cylinder
00:15:21.100 --> 00:15:28.010
for virtue of this particular geometrical
condition is 2 pi R, that is the perimeter
00:15:28.010 --> 00:15:34.329
into the L . And, now this will be the
intensity. So, suppose a length of the source
00:15:34.329 --> 00:15:42.550
is 100 meter output is 0.005 watt what will
be the SPL at 7 meter from the line source.
00:15:42.550 --> 00:15:48.850
So, this we just convert with that I got this
particle intensity level and again I will
00:15:48.850 --> 00:15:55.420
take the particular equation intensity or
the intensity reference, I will get 60.5 dB
00:15:55.420 --> 00:16:03.420
as the the decibel level .
Now, from the line source If, I go R 1 distance
00:16:03.420 --> 00:16:10.370
from R 1 distance while get the intensity
as the the cylinder of the radius R 1 of length
00:16:10.370 --> 00:16:18.779
L, if I go to R 2 I get this value of I 2
and let us find find out the what is the difference
00:16:18.779 --> 00:16:25.730
between the L the level at the at a
distance R 1 and R 2 . And I know this R 1
00:16:25.730 --> 00:16:30.230
will be higher the level sound level at this
is higher, because it is nearer to the source.
00:16:30.230 --> 00:16:35.579
So, again I will take the operation of that
and very similarly I can find out the what
00:16:35.579 --> 00:16:41.720
will be the values of I 1 and I 2 from here
and what is the difference between the SPL
00:16:41.720 --> 00:16:50.839
a modern SPL 2 and this gives me a formula
like SPL 1 and SPL 2 is 10 log or 2 by R 1
00:16:50.839 --> 00:16:58.290
. And, if the distance is doubled suppose
R 2 is twice of R 1 then this is 10 log 2,
00:16:58.290 --> 00:17:02.570
which is 3 dB .
So, if it is a cylindrical propagation, if
00:17:02.570 --> 00:17:08.979
the distance is doubled, the dB level drop
by 3 dB, but if you remember in the in the
00:17:08.979 --> 00:17:16.019
in the the spherical propagation it was 6
dB . So, next let us go to the near and far
00:17:16.019 --> 00:17:21.019
field propagation.
Suppose it is a it is a the the BC road
00:17:21.019 --> 00:17:24.189
sections and that is gives me a cylindrical
propagation.
00:17:24.189 --> 00:17:31.479
But, why virtue of this propagation if you
now go further in this away from the this
00:17:31.479 --> 00:17:38.779
line away from the road . This way front is
again going to get a spherical of suppose,
00:17:38.779 --> 00:17:46.009
if you are very standing very far distance
from the road since road noise will be act
00:17:46.009 --> 00:17:53.289
as a point source 1 ones again.
So, some point source gives you a line source
00:17:53.289 --> 00:17:57.830
and if you are very near to that particular
line source this is a cylindrical propagation.
00:17:57.830 --> 00:18:05.549
And, now if you go further that particular
line will act as a point and then it is trans
00:18:05.549 --> 00:18:14.409
form to a or to a thus spherical propagation.
So, there is a near field zone and there is
00:18:14.409 --> 00:18:20.520
a transition zone and there are the far field.
So, what happened in the far field zone? In
00:18:20.520 --> 00:18:28.289
the far field zone sound is spherical propagation
sound the the sound propagation is spherical
00:18:28.289 --> 00:18:32.370
. What happened in the near field zone the
propagation is cylindrical?
00:18:32.370 --> 00:18:37.899
So, if in this near field zone I want to calculate
something I have to assume that this source
00:18:37.899 --> 00:18:44.000
is a cylinder linear source propagation
is cylindrical . Suppose I am here, if I want
00:18:44.000 --> 00:18:49.289
to find out the same effect of this particular
road noise, then I have to assume this as
00:18:49.289 --> 00:18:54.379
a point source. And I have to assume this
is as a spherical propagation.
00:18:54.379 --> 00:19:01.710
So, if the spherical and the cylindrical propagation
or the near field and the th far field has
00:19:01.710 --> 00:19:07.879
to be taken into account. So, in the near
field zone it is drop by 3 dB by if the developed
00:19:07.879 --> 00:19:14.729
the distance and in the far field which is
spherical is 6 GB as per the distance is doubled.
00:19:14.729 --> 00:19:20.989
So, by virtue of this there are 2 type of
sources in case of any kind of the analysis
00:19:20.989 --> 00:19:28.320
or any kind of the the measurement, if
you take for any kind of sound at in the
00:19:28.320 --> 00:19:33.169
the environmental sound. Then you have
to know that we were in a far field or your
00:19:33.169 --> 00:19:39.519
in a near field and you have to take the specific
formula, and you to take the specific condition
00:19:39.519 --> 00:19:46.369
and then analyzed .
Now, next go to the the loudness, loudness
00:19:46.369 --> 00:19:52.740
is a combination of the frequency and the
SPL . Now, what happened if in the X axis
00:19:52.740 --> 00:19:58.679
I have marked the all the octave band frequencies,
it is the starting from the 31.5 to the 16,000
00:19:58.679 --> 00:20:04.950
. And the SPL is actually written in the Y
axis that is in the dB.
00:20:04.950 --> 00:20:12.740
Now, the human being perceive sound differently
suppose I plot some points. The first point
00:20:12.740 --> 00:20:20.659
let us see this is the when 1000 hertz and
60 dB, it is gives me some kind of sensation,
00:20:20.659 --> 00:20:27.330
some kind of sensation. And the sensation
is very similar, when the the frequency of
00:20:27.330 --> 00:20:36.179
the sound is 125 dP and more or less 65
65 dB and 125 hertz.
00:20:36.179 --> 00:20:44.979
Sorry 125 hertz sound with 65 dB for 63 hertz,
the same sensation what I am experiencing
00:20:44.979 --> 00:20:52.570
here? I am getting the same sensation for
63 hertz at around 80 dB . So, if I just plot
00:20:52.570 --> 00:21:00.990
all those point, which gives me a same similar
type of sensation, with respect to 1000 hertz
00:21:00.990 --> 00:21:08.559
and some amount of dB and I can actually create
a contour line or a kind of a line.
00:21:08.559 --> 00:21:16.210
And, this is a kind of a loudness it is a
similar loudness or the same loudness . So,
00:21:16.210 --> 00:21:24.340
loudness of the sound is vary from with this
2 fundamental parameter of frequency and the
00:21:24.340 --> 00:21:34.759
SPL. So, this is the loudness and corresponding
to this 1000 and 60, the loudness is this
00:21:34.759 --> 00:21:42.840
particular loudness graph is called 60 Phon.
So, by definition 1 Phon is equal to 1 dB
00:21:42.840 --> 00:21:50.039
at 1000 hertz .
Similarly, can plot lot of such plots of in
00:21:50.039 --> 00:21:57.080
the frequency and the SPL level so, it is
starts from 10, which is threshold of audibility
00:21:57.080 --> 00:22:04.899
and it is goes up to 100 may be 120 also,
which is the threshold pen and those blue
00:22:04.899 --> 00:22:14.850
numbers are your Phons and this red lines
are of your the equal or loudness path or
00:22:14.850 --> 00:22:21.220
the equal loudness contour .
So, you see in this I can say that this
00:22:21.220 --> 00:22:30.779
particular band, which is 2000 to 8000 hertz
is very sensitive this frequency is very sensitive
00:22:30.779 --> 00:22:37.059
to our here, because you see this loudness
contour curve dipping in dipping over here.
00:22:37.059 --> 00:22:47.609
So, even a smallest amount of smallest amount
of loudness can here in this particular frequency
00:22:47.609 --> 00:22:56.239
zone . So, suppose if you want to here is
6 of 30 dB sound of this 4000, you required
00:22:56.239 --> 00:23:04.479
this much of the sound level 22, but same
with 63 you required almost about 60 dB you
00:23:04.479 --> 00:23:14.919
cannot here, you cannot here . So, 30
loudness sound this is the equal loudness
00:23:14.919 --> 00:23:19.519
contour also.
Now, how this loudness can be measured. So,
00:23:19.519 --> 00:23:25.929
suppose I say that I have a sound from a source
which gives me 40 Phon. So, this is the curve
00:23:25.929 --> 00:23:32.389
and another source gives me 60 Phon. So, this
is the curve. So, can I say if I though both
00:23:32.389 --> 00:23:40.629
the sound source if it is on switch on, the
final sound which is combination of 60 and
00:23:40.629 --> 00:23:48.690
40 the Phon is equal to 100 no it cannot be,
it cannot be added like that be, because this
00:23:48.690 --> 00:23:55.029
phon is a is a not it it is not a physical
parameter. It is a kind of a psychological
00:23:55.029 --> 00:24:01.330
parameter, what a human being is receive?
Suppose this particular graph which we have
00:24:01.330 --> 00:24:07.590
shown you, this is equal loudness contour
is for a young gentleman. Suppose, if you
00:24:07.590 --> 00:24:15.859
do the same experiment with a the old person
of around age of 75 or so, this graph will
00:24:15.859 --> 00:24:22.869
be shrink a bit he or she will perceive
a different way different type of sum
00:24:22.869 --> 00:24:29.019
graph some some some contour and maybe omitted.
He or she may not here that particular phon.
00:24:29.019 --> 00:24:36.639
So, it is fully psychologically or how the
brain is going to map my the sound,
00:24:36.639 --> 00:24:42.809
that way it particular it is devised or
it is actually analyzed and derived. And that
00:24:42.809 --> 00:24:51.090
is why this the unit of loudness this is
phon cannot be added and it is not be justified
00:24:51.090 --> 00:24:58.159
to add like that. So, we need to add because
there are 2 different loudness and why and
00:24:58.159 --> 00:25:02.469
this 2 different loudness has to be added
to give a resultant count if the sound loudness.
00:25:02.469 --> 00:25:09.019
So, we have to take another scale and that
scale should be little bit of a linear scale
00:25:09.019 --> 00:25:16.679
and that scale is called Sone scale. And in
loudness 10 phon increase gives a increment
00:25:16.679 --> 00:25:23.419
of the twice of multiplication factor of the
sone. So, if I see this is the loudness loudness
00:25:23.419 --> 00:25:29.669
plot that is the from 10 to 100 phon, the
corresponding and this cannot be added this
00:25:29.669 --> 00:25:34.859
phon cannot be added.
So, this corresponding phon can be translated
00:25:34.859 --> 00:25:44.279
to a linear format of sone, which is showing
here in a blue numbers. So, the forty phon
00:25:44.279 --> 00:25:52.469
is converted to 1 Sone and correspondingly,
if you go to the next higher phon of 10 phon
00:25:52.469 --> 00:26:02.090
higher 50, it is multiplied by 2 . If go to
another 10 higher 60 this 2 is multiplied
00:26:02.090 --> 00:26:10.999
by 2 4 and then 8 16 like that.
So, the 100 phon is equivalent to 64 Sone
00:26:10.999 --> 00:26:19.279
and now if you go beyond b 1 in below 40
by 10 phon recruitment we have to divide this
00:26:19.279 --> 00:26:31.369
1 by 2.5, another 10 decrease 20 from 30.5
divided by 2.25 like that . So, it can be,
00:26:31.369 --> 00:26:39.679
now mathematically express like Sone is 2
to the power phon minus 40 by 10 just put
00:26:39.679 --> 00:26:48.369
suppose 60, if you put 60 over here 60 minus
40 is 20, 20 by 10 is to 2 to the power 2
00:26:48.369 --> 00:26:51.889
is 4.
Something like that you can with this particular
00:26:51.889 --> 00:27:00.049
formula we can find out . And in the
reciprocal way a phon can be find out by just
00:27:00.049 --> 00:27:06.600
virtue of this particular equation . So, you
just if you want to find out what is 16
00:27:06.600 --> 00:27:15.590
Sone equivalent phon put 16 here log 16 multiplied
by 33.2 2 and add 40 into it .
00:27:15.590 --> 00:27:25.979
So, now we can actually go into this particular
measurement. Now forty gives me 1, because
00:27:25.979 --> 00:27:34.259
I put 40 over here. So, this is 1 very similarly
I convert this 60 phon to it is corresponding
00:27:34.259 --> 00:27:42.190
Sone level which is 4.
Now, I cannot add phon 60 plus 40 cannot be
00:27:42.190 --> 00:27:50.759
100, but I can add this sone. So, 4 plus 1
is 5 total sone, because of this 2 is 5. And
00:27:50.759 --> 00:27:59.789
as I got this 5 Sone is the resultant Sone
I can convert that Sone to the phon by that
00:27:59.789 --> 00:28:09.149
equation I put this Sone as 5 log of 5
into 33.2 2 and I add with that with 40,
00:28:09.149 --> 00:28:15.090
it is 63 .
So, I can say it is not 100 phon, if you
00:28:15.090 --> 00:28:24.909
add 40 and 60 it is 63 . So, that is ends
this particular chapter this particular
00:28:24.909 --> 00:28:31.799
lecture number 5, which is about the near
and far field propagation and also about the
00:28:31.799 --> 00:28:39.549
loudness and this fifth lecture also include
the first week of our architectural acoustics
00:28:39.549 --> 00:28:47.479
course, online course and this total 5 lectures
comprises of some historical development of
00:28:47.479 --> 00:28:54.649
the sound from the different era, which
Doctor Suman Gupta has discussed in the
00:28:54.649 --> 00:29:01.489
very first day, and are very first lecture,
and then the 4 consecutive lecture on the
00:29:01.489 --> 00:29:06.789
pure acoustical physics are the building physics.
So, at the end of this lecture let us have
00:29:06.789 --> 00:29:11.950
once again some homework and take away to
your home let us try this.
00:29:11.950 --> 00:29:17.879
The try this particular the formula the
sorry this particular problem because this
00:29:17.879 --> 00:29:23.249
will give you a kind of a understanding between
the near field and far field, suppose a the
00:29:23.249 --> 00:29:31.799
sound intensity level S I L and is 10 meter
from the sound source SIL at at a distance
00:29:31.799 --> 00:29:37.399
10 meter from the sound source, you have to
find out what will be the the SIL at the 10
00:29:37.399 --> 00:29:44.100
meter from the sound source. If the SIL at
3 meter from the sound source is 75 GB and
00:29:44.100 --> 00:29:48.599
first of all you assume it is the near field
propagation, where the sound propagate in
00:29:48.599 --> 00:29:53.809
a cylindrical form and in second case you
assume that has a far field propagation.
00:29:53.809 --> 00:29:59.799
So, that is a spherical wave. So, in this
particular videos or in this particular PPT
00:29:59.799 --> 00:30:05.820
is is sometimes you may sit is a S I L I have
written sometimes it is SPL, a sound pressure
00:30:05.820 --> 00:30:12.309
level or sound intensity level, both are actually
going to give in dB scale and these are related.
00:30:12.309 --> 00:30:18.759
So, do not be confused with that thus it is
name suggest, it is sound intensity level
00:30:18.759 --> 00:30:23.940
and sometimes it is sound pressure level,
but finally, by computation end result is
00:30:23.940 --> 00:30:29.019
dB is the same .
Take a second problem also for your homework,
00:30:29.019 --> 00:30:37.039
that is can you find out the loudness of 2
different sound parameter, sound
00:30:37.039 --> 00:30:45.950
source a gives you a frequency of 250 hertz
and SPL of 60 Db, definitely this 2 combinations
00:30:45.950 --> 00:30:53.649
gives you some kind of a phon and a sound
level a sound source be gives you a of a frequency
00:30:53.649 --> 00:31:01.649
of 4 kilo hertz and SPL of 70 dB, that
also converted to a particular the phon
00:31:01.649 --> 00:31:07.979
in loudness contour and then you add this
2 together both the the sound source A and
00:31:07.979 --> 00:31:12.499
sound source B.
The effective or the resultant the loudness
00:31:12.499 --> 00:31:20.629
you have to find out . So, those are the
references and that is the end of the lecture
00:31:20.629 --> 00:31:27.119
number 5, hope you understand the lecture
well and if you not go through the lecture
00:31:27.119 --> 00:31:31.619
once more and you can also contact us and.
Thank you very much .