WEBVTT
Kind: captions
Language: en
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.
Ah Good morning everybody . So, today we will
00:00:19.170 --> 00:00:25.480
going to start the lecture number 4 and the
module number 1. in the first week module
00:00:25.480 --> 00:00:30.660
. So, today we will going to discuss about
the sound pressure and the intensity level.
00:00:30.660 --> 00:00:36.190
If you remember in the last two lecture what
we have discuss is that is the propagation
00:00:36.190 --> 00:00:40.650
of the sound, we also discuss the frequency
and the octave band.
00:00:40.650 --> 00:00:46.960
So, now, let us proceed further and let us
know what is the sound pressure and how it
00:00:46.960 --> 00:00:53.920
can be measure and how that particular sound
pressure and the sound intensity can be
00:00:53.920 --> 00:01:02.680
mathematically converted to the sound levels.
So, in this lecture we have again two objective
00:01:02.680 --> 00:01:07.610
as a learning objective. So, what you will
want to do in this particular half an hour
00:01:07.610 --> 00:01:13.360
lecture is that, we need to convert or we
need to know how to convert the intensity
00:01:13.360 --> 00:01:19.469
and the pressure to a particular sound level
and also we will like to know that how
00:01:19.469 --> 00:01:25.590
can this particular sound levels of from the
multiple sources can be added and what will
00:01:25.590 --> 00:01:31.299
be the result and sound level for that the
for the additional all.
00:01:31.299 --> 00:01:38.429
So, here we need some kind of operation,
some kind of a mathematical operation to know
00:01:38.429 --> 00:01:45.359
about. And this mathematical operations are
well known to you, but that for the the
00:01:45.359 --> 00:01:51.139
the starting point of view, let us brush up
those mathematical operations and we need
00:01:51.139 --> 00:01:57.259
here some logarithmic operation .
In the logarithmic operation the first operation
00:01:57.259 --> 00:02:03.520
is something like this, which is also you
know that is log a if it is x, then 10 to
00:02:03.520 --> 00:02:10.260
the power x it is equal to a. The next operation
what we also need is that if though 2 log
00:02:10.260 --> 00:02:14.810
terms are added.
Suppose log a plus log b, it will be log a
00:02:14.810 --> 00:02:20.760
b. The third operation what we need is that
is the subtraction from one to another log;
00:02:20.760 --> 00:02:28.239
that means, log a minus log b will be reciprocal
that is the log a by will b log a by
00:02:28.239 --> 00:02:33.680
b; and the third or the fourth one and the
last one what we need is that if log a to
00:02:33.680 --> 00:02:40.739
the power n is always equal to n into log
a . So, this four basic operation of log will
00:02:40.739 --> 00:02:45.750
be required to understand the basic principles
of the sound pressure level and the sound
00:02:45.750 --> 00:02:52.459
intensity level . Now, let us know how
we actually here human hearing.
00:02:52.459 --> 00:02:59.150
So, what we see in this particular board
is that, the cross section of human ear. You
00:02:59.150 --> 00:03:03.799
must have seen this particular cross section
of the human ear in your school days in your
00:03:03.799 --> 00:03:11.930
biology book . So, here as we understand
from the first lecture is the sound is a wave
00:03:11.930 --> 00:03:19.280
transmission, and that wave transmission gives
in the ear in a multiple layer, which
00:03:19.280 --> 00:03:24.829
will some layer will be compressed and the
the next layer will be radar fact or the
00:03:24.829 --> 00:03:28.580
extend and it will move from one point to
the other .
00:03:28.580 --> 00:03:33.879
So, when it moves from one point to the other,
the wave propagation towards the if it is
00:03:33.879 --> 00:03:39.120
towards the ear it will enter into our ear
and how it will actually sense the brain,
00:03:39.120 --> 00:03:42.799
let us discuss that .
Suppose this is the ear cross section, the
00:03:42.799 --> 00:03:48.280
similar ear cross section and it has some
some some part. So, these four parts are may
00:03:48.280 --> 00:03:54.249
be the first three parts are called as a the
the the outer ear part, which is has a pinna
00:03:54.249 --> 00:04:00.030
which is like this and then there is a auditory
canal over there and then auditory canal is
00:04:00.030 --> 00:04:05.680
actually terminated to the eardrum. And if
there is a particular propagation and if
00:04:05.680 --> 00:04:14.540
I am I am showing it in a flow chart diagram,
the external ear that is from here, the pressure
00:04:14.540 --> 00:04:19.970
which followed by a follow the path of the
auditory canal and it will strike to the the
00:04:19.970 --> 00:04:27.040
eardrum. And the total pressure of the particular
channel or the canal auditory canal is equal
00:04:27.040 --> 00:04:31.640
to the atmospheric pressure plus the sound
pressure.
00:04:31.640 --> 00:04:39.120
The P atmospheric plus P s and it will strikes
to the ear drum. And there is a another cannel
00:04:39.120 --> 00:04:45.760
or another tube that is there in through our
mouth to the the to the cannel. So, that is
00:04:45.760 --> 00:04:51.560
called as a the eustachian tube and this eustachian
tube will only take care of the atmospheric
00:04:51.560 --> 00:04:57.510
pressure, and it will also proceed to the
ear drum. If you see I have animated a
00:04:57.510 --> 00:05:05.180
bit, this particular this the the the the
red arrows or the pressure from the air pressure
00:05:05.180 --> 00:05:10.340
that is the atmospheric pressure and the the
sound pressure and another the yellow arrows
00:05:10.340 --> 00:05:13.130
from the eeustachian is the only atmospheric
pressure.
00:05:13.130 --> 00:05:20.650
So, the ear drum basically under two different
pressure scenario, one is P atmospheric and
00:05:20.650 --> 00:05:28.010
plus P sound and from other side it is P atmospheric.
So, finally, the ear drum will vibrate because
00:05:28.010 --> 00:05:33.850
of the the resultant pressure of that, that
is two the P sound pressure that
00:05:33.850 --> 00:05:42.340
is the the two mutually perpendicular
and and opposite directional not
00:05:42.340 --> 00:05:48.710
perpendicular, mutually in a in a in
a linear and a opposite indirection. So, the
00:05:48.710 --> 00:05:53.810
sound pressure, will the P s will actually
vibrate the eardrum. What happened in the
00:05:53.810 --> 00:05:59.770
next operation is that.
So, this ear drum is connected by the three
00:05:59.770 --> 00:06:05.610
is middle ears very small bones and there
are three bones malleus incus and stapes is
00:06:05.610 --> 00:06:13.000
linked one after another, and that is actually
transmitting the the transmitting
00:06:13.000 --> 00:06:16.630
the particular the three ear bones to the
cochlea.
00:06:16.630 --> 00:06:21.860
And cochlea is full of some liquid or so.
So what happened is that, when this ear drum
00:06:21.860 --> 00:06:27.270
is vibrate by the sound pressure it will going
to vibrate the middle ear bones this three
00:06:27.270 --> 00:06:32.610
bones and there is a micro amplification,
micromechanical amplification I must say,
00:06:32.610 --> 00:06:37.740
because this is a three bones are a hinge
together and it will be the amplify the thing
00:06:37.740 --> 00:06:43.890
and it will be actually impulse has been provided
to the cochlea. And this three are the bones
00:06:43.890 --> 00:06:51.220
and the cochlea are called the the in interior
part of the ear and then finally, cochlea
00:06:51.220 --> 00:06:56.680
sense that, cochlea sense that and then it
is the behind the cochlea there are auditory
00:06:56.680 --> 00:07:00.750
nerves.
So, there the cochlea sense that particular
00:07:00.750 --> 00:07:07.050
vibration from the three middle ear bone and
it provide the some mechanico electrico kind
00:07:07.050 --> 00:07:14.140
of a conversion, the mechanical to the electrical
conversion and this electrical sensor pulses
00:07:14.140 --> 00:07:17.740
through the nerve it will sense in our bend
.
00:07:17.740 --> 00:07:24.240
So, this is at a go, we can actually again
see that particular flow chart. So, this
00:07:24.240 --> 00:07:29.110
is the ear drum vibrate by P s that is the
pressure from the sound, sound pressure than
00:07:29.110 --> 00:07:36.030
middle ear vibrate micromechanical amplification
gives to the cochlea, from the cochlea a mechanico
00:07:36.030 --> 00:07:43.620
electrico conversion and then it is going
through the the auditory nerve to the
00:07:43.620 --> 00:07:48.170
brain .
Now next is let us see the how the brain
00:07:48.170 --> 00:07:56.640
and our sensation of the sound is perceive
by the brain. A psychologist weber suggested
00:07:56.640 --> 00:08:02.370
this particular phenomena or this particular
proposition, that is the subjective response
00:08:02.370 --> 00:08:07.840
is the function of change of stimulate is
proportional. So, if it is proportional. So,
00:08:07.840 --> 00:08:13.970
if it is something like a the change of
responses R, this response may be the weight,
00:08:13.970 --> 00:08:18.920
this response may be the light, there is a
slight change in the light whether I can identify
00:08:18.920 --> 00:08:24.200
that particular change or not, if there is
a weight in my hand I just increase a bit
00:08:24.200 --> 00:08:30.080
of extra weight can I sense that one that
is the stimuli the change of the stimuli and
00:08:30.080 --> 00:08:34.390
the R is the sense.
So, mathematically it can be expressed as
00:08:34.390 --> 00:08:41.219
the the change of R is equal to change of
stimuli by the act the the initial stimuli
00:08:41.219 --> 00:08:48.130
that is the cap S. If I integrate then this
two side, then I will get a mathematical expression
00:08:48.130 --> 00:08:54.970
like the R is equal to log of S and there
is a integration constant are C and then further,
00:08:54.970 --> 00:09:01.510
this integration constant constant C can be
clubbed into this logarithmic part also, and
00:09:01.510 --> 00:09:09.190
then we can write that R is equal to k times
log of S. So, this is a particular way the
00:09:09.190 --> 00:09:16.210
human being sense for weight for any scenario
like a light or may be temperature or maybe
00:09:16.210 --> 00:09:20.360
the sound.
And we see that in the sound in in in case
00:09:20.360 --> 00:09:28.900
of a the auditory case auditory sensation,
we can sense the very minute change not in
00:09:28.900 --> 00:09:34.930
a specific way, but if there is a change in
a bigger order then it may be sense in a better
00:09:34.930 --> 00:09:42.670
way. And this particular change is very much
adopted or very much sensible if the frequency
00:09:42.670 --> 00:09:48.750
or the level of the sound is in the lower
order. This particular change the same change
00:09:48.750 --> 00:09:52.500
if it is in a higher order, we may not sense
that one.
00:09:52.500 --> 00:10:00.450
So, that is why we can say finally, that a
human being or a we here logarithmic. So,
00:10:00.450 --> 00:10:06.980
the expression of the sensation that is the
sound pressure or the sound intensity finally,
00:10:06.980 --> 00:10:12.240
translated to a logarithmic scale and that
will give us the sensation, what we have just
00:10:12.240 --> 00:10:18.140
now discussed or the see from this particular
webers proposition .
00:10:18.140 --> 00:10:24.100
So, let us take a graph and in the the
the y axis let us have the sound pressure
00:10:24.100 --> 00:10:33.750
starting from 2 to 2 into 10 to the power
minus 5 mega pascal 220. So, it is a huge
00:10:33.750 --> 00:10:45.190
range huge range. So, almost 10 to the power
7 a 6times of the the the sound pressure
00:10:45.190 --> 00:10:50.570
changes and in a another side let us write
down the sound intensity and as you know the
00:10:50.570 --> 00:10:55.529
intensity is the watt per meter square or
the power per particular square print of
00:10:55.529 --> 00:11:01.960
the the foot print of the area.
So, they are also it is equivalent to 10 to
00:11:01.960 --> 00:11:10.870
the power minus 12 watt per meter square two
one watt per meter square. It is almost about
00:11:10.870 --> 00:11:18.060
10 to the power 12 times higher from the lower
to the higher level. And if the sensation
00:11:18.060 --> 00:11:33.410
or the sound pressure which is actually followed
and to enter to our the enter to our ear is
00:11:33.410 --> 00:11:44.560
at around 2 into 10 to the power minus 5 newton
per mm square or in the intensity terms 10
00:11:44.560 --> 00:11:49.730
to the power minus 12 watt per meter square.
We start hearing that is the minimum amount
00:11:49.730 --> 00:11:56.410
of the the intensity level or the minimum
amount of pressure sound pressure is is needed
00:11:56.410 --> 00:12:02.630
to the the human being to hear some sound
and that is why it is called the threshold
00:12:02.630 --> 00:12:08.839
of audibility . So, if the sound pressure
level is below that, we we cannot response
00:12:08.839 --> 00:12:14.580
that the the to that particular sound. And
if it is higher than 2 to the power 10 to
00:12:14.580 --> 00:12:21.650
2 into 10 to the power minus 5 yes we hear
better, and further better if the intensity
00:12:21.650 --> 00:12:29.640
and the sound pressure is further up , but
there is the limit.
00:12:29.640 --> 00:12:37.160
If the particular pressure is 20 newton per
mm square or the intensity is one watt per
00:12:37.160 --> 00:12:43.960
meter square, then it is start paining to
our eye paining to our ear and that is
00:12:43.960 --> 00:12:48.061
very very comfortable, and that particular
point or that particular intensity is called
00:12:48.061 --> 00:12:52.850
the threshold of pain it is the discount foster.
Sometimes it is also referred as the threshold
00:12:52.850 --> 00:12:59.200
of this discomfort and further it may go
further, it may go further 10 to 12 12 to
00:12:59.200 --> 00:13:03.420
15 percent further, but it will start giving
lot of problem to our ear and finally, the
00:13:03.420 --> 00:13:07.980
ear drum may rapture and that is going to
be a serious concern.
00:13:07.980 --> 00:13:12.480
So, we will try to limit our the hearing
pressure level, this 2 into 10 to the power
00:13:12.480 --> 00:13:19.960
minus 5 to 2 20 and the intensity level 10
to the power minus 12 to 1 watt per meter
00:13:19.960 --> 00:13:24.890
square. Now this are the some physical factor
or the physical parameter, we have to translate
00:13:24.890 --> 00:13:28.740
this physical parameter to a sound pressure
level or the sound intensity level.
00:13:28.740 --> 00:13:31.540
So, let us see the what is the sound intensity
level . So, this graph and in this graph what
00:13:31.540 --> 00:13:34.500
happened is that, the sound intensity level
which is called as a SIL is defined as logarithmic
00:13:34.500 --> 00:13:40.500
of I by I reference and if it is so, it is
called bell and if it is 10 into logarithmic
00:13:40.500 --> 00:13:46.380
of I by I reference its called disable. Now
what is I and what is I reference let me see.
00:13:46.380 --> 00:13:50.370
The I reference is the minimum level of the
the pressure or the intensity, that we
00:13:50.370 --> 00:13:53.490
required for the threshold of audibility . So,
this is that particular 10 to the power minus
00:13:53.490 --> 00:14:03.730
12 watt per meter square and what is I? The
actual intensity of that of the sound. So,
00:14:03.730 --> 00:14:11.850
suppose I am going to calculate some intensity
which is in between 1 and 10 to the power
00:14:11.850 --> 00:14:14.610
minus 12. So, that suppose 10 to the power
minus 5.
00:14:14.610 --> 00:14:25.190
So, the I value of I will be 10 to the power
minus 5 also . So, here from here let us see
00:14:25.190 --> 00:14:37.410
if the if the if the the sound pressure is
10 to the power minus 12 . So, then it is
00:14:37.410 --> 00:14:43.410
one this logarithmic value is one the log
1 is 0. So, the it is 0 decibel almost no
00:14:43.410 --> 00:14:47.710
sound just starting of the audibility. And
if it is the higher suppose it is 1.
00:14:47.710 --> 00:14:55.610
So, I put one over 10 to the power minus 12
over here, I may say take the logarithmic
00:14:55.610 --> 00:15:00.740
and multiply with 10 this is 120 disable . So,
it is painful its threshold of pain is 120
00:15:00.740 --> 00:15:07.480
almost we may go up 240 also and this is very
much painful and very much not not that much
00:15:07.480 --> 00:15:13.399
that the hygienic and the peak going to rapture
the the ear drum or so .
00:15:13.399 --> 00:15:15.970
Very similarly we can find out the sound power
level also. Sound power level is also define
00:15:15.970 --> 00:15:21.920
in a same way in a decibel scale log of W
by W reference into 10. And this w reference
00:15:21.920 --> 00:15:28.010
is 10 to the power minus 12 watt because power
the the the unit of power is watt, and it
00:15:28.010 --> 00:15:33.980
goes up to 10 the 1 watt or so, where there
is a and if you convert the same way it is
00:15:33.980 --> 00:15:37.050
0 and 120.
Now, let us see the sound pressure level which
00:15:37.050 --> 00:15:41.899
we have just discussed in the the first graph.
The sound pressure is again fluctuating from
00:15:41.899 --> 00:15:45.770
2 into 10 to the power minus 10 to 20, and
sound pressure level is defined as not 10,
00:15:45.770 --> 00:15:49.230
but 20 into logarithmic of P by P reference
as the intensity and pressure is related with
00:15:49.230 --> 00:15:55.140
the proportionally is pressure square the
intensity is proportional to the square of
00:15:55.140 --> 00:15:56.240
the pressure.
So, how it is we will discuss in the fifth
00:15:56.240 --> 00:15:57.340
lecture and how it is actually the the proportional
to the pressure square. So, here also the
00:15:57.340 --> 00:16:01.370
similar manner we can find out the our P reference
is that the minimum, which is the threshold
00:16:01.370 --> 00:16:03.610
of audibility which is 2 into 10 to the power
minus 5, the P the whatever may be the value
00:16:03.610 --> 00:16:11.560
of the pressure that I will put over here,
and if it is 20 that is the highest level
00:16:11.560 --> 00:16:16.960
if I put 20 by 2 into 10 to the power minus
10 log and multiply by 20 its gives me 120
00:16:16.960 --> 00:16:23.110
disable . So, by virtue of this if I go back
and then we have derived the intensity
00:16:23.110 --> 00:16:26.990
level, we have derived the power level, we
have derived the sound pressure level and
00:16:26.990 --> 00:16:29.420
all are in decibels .
So, the y decibel y decibel because the we
00:16:29.420 --> 00:16:33.930
we everybody knows the Alexander Graham
Bell on the honor to his name honor to
00:16:33.930 --> 00:16:38.660
his scientific development in our the the
world community we have or the the scientific
00:16:38.660 --> 00:16:42.290
community has proposed the the unit of the
the sound pressure level as bell or decibel.
00:16:42.290 --> 00:16:45.740
And in the left hand side you will see that
from instrument, which is the sound level
00:16:45.740 --> 00:16:50.720
meter and the sound level meter is used for
the measuring the sound level that is in decibel
00:16:50.720 --> 00:16:52.820
or so.
So I have a sound level meter with me and
00:16:52.820 --> 00:16:57.600
if you see this sound level meter it has a
power button. So, you have to switch on the
00:16:57.600 --> 00:17:03.420
power button and then there is a the
range you can said the range, we can said
00:17:03.420 --> 00:17:09.949
the range from the minimum to the medium to
the maximum and there is a microphone attach
00:17:09.949 --> 00:17:14.651
to this particular the the the arm on the
top and as you see I am speaking. So, this
00:17:14.651 --> 00:17:19.559
is going to be be some kind of the the
sound pressure level.
00:17:19.559 --> 00:17:22.399
Now, it is 65 70 68 68 62 like that . So,
. So, some sound it will catch and then
00:17:22.399 --> 00:17:26.799
it will going to give you the sound pressure
level directly .
00:17:26.799 --> 00:17:30.700
So, the sound intensity to the sound level
conversion. So, now, let us play with those
00:17:30.700 --> 00:17:34.769
formula and see how the sound intensity and
the sound pressure and the sound pressure
00:17:34.769 --> 00:17:39.529
to the intensity or those levels can be taken
into consideration. So, here in this slide
00:17:39.529 --> 00:17:43.000
we will discuss the sound intensity . So,
the sound level conversion. So, as we know
00:17:43.000 --> 00:17:52.090
this is the formula the level L is equal to
10 into the logarithmic of I by I reference.
00:17:52.090 --> 00:17:56.570
So, I have a small small very small problem
that suppose the intensity is 0.005 watt per
00:17:56.570 --> 00:18:04.309
meter square what would be the intensity.
So, as you put it everything in the value,
00:18:04.309 --> 00:18:08.360
everything in this particular every value
in the particular formula and the get the
00:18:08.360 --> 00:18:13.500
ratio and multiply with the 10 log and multiply
with the 10 and you get 97 dB which is pretty
00:18:13.500 --> 00:18:16.830
high .
Then the the reverse order the sound level
00:18:16.830 --> 00:18:20.700
to sound intensity conversion. So, the
sound level to sound intensity conversion
00:18:20.700 --> 00:18:27.879
you have the same formula and from the formula,
you derive like the then the log of I by I
00:18:27.879 --> 00:18:36.999
reference will be [laughter] by 10, because
you see the if you just go with this formula
00:18:36.999 --> 00:18:46.700
and then if it is I by I reference will be
10 to the power L by 10 and finally, I am
00:18:46.700 --> 00:18:56.350
interested to find out the I. So, the I will
be equal to I reference into 10 to the power
00:18:56.350 --> 00:19:08.269
L by 10.
I reference we all know that is 10 to the
00:19:08.269 --> 00:19:13.610
power minus 12 and l is the sound level that
is d|B how much is the decibel that you can
00:19:13.610 --> 00:19:21.489
put and finally, we can find out what is the
value of i. So, suppose a a SIL of the sound
00:19:21.489 --> 00:19:32.280
intensity level is 65. So, I will put 65 over
here. So, finally, it is 10 to the power
00:19:32.280 --> 00:19:37.649
6.5 and the I reference is your 10 to the
power minus 12. So, finally, this is the watt
00:19:37.649 --> 00:19:45.019
per meter square that is the the intensity
.
00:19:45.019 --> 00:19:54.190
So, I have listed down some intensity
or the sound level in fact, in the dB just
00:19:54.190 --> 00:20:05.710
to give you a kind of a idea that what is
the dB that exist in our day to day life.
00:20:05.710 --> 00:20:15.970
You sweeping of the dry lips is very very
low level of or the sound which is around
00:20:15.970 --> 00:20:22.340
10 15 or so, background noise in the television
studio where there is kind of a broadcasting
00:20:22.340 --> 00:20:30.999
or may be telecasting is of of a happening
over there, we required very low amount of
00:20:30.999 --> 00:20:34.950
sound level which is prescribed as 20 decibel.
Library, very quit area, bedroom very quit
00:20:34.950 --> 00:20:38.250
area 30 to 40 is recommended, residential
zone recommended as 50, now normal conversation
00:20:38.250 --> 00:20:43.789
which we are doing now it is more or less
60 we have seen in this sound level meter
00:20:43.789 --> 00:20:47.529
60 to 70 it is fluctuating. Vacuum cleaner,
vacuum cleaner is a sound produce producing
00:20:47.529 --> 00:20:53.929
the equipment which is if you in front
of one meter of that particular vacuum
00:20:53.929 --> 00:21:00.450
cleaner gives you around 70. Heavy city traffic
is 80; the pneumatic drill is very bothering
00:21:00.450 --> 00:21:07.330
sometimes it is the 90 to 100. The discotheque
it is the noise area very noise area in fact,
00:21:07.330 --> 00:21:10.410
and its almost touching to the the threshold
of pain sometimes it is 100 to 110 and if
00:21:10.410 --> 00:21:16.549
it you if it is very near to jet aircraft,
around 100 meter net to jet aircraft it is
00:21:16.549 --> 00:21:21.840
really painful 140 .
Now let us see the the how the addition of
00:21:21.840 --> 00:21:26.159
sound levels can be done. So, I actually have
to encounter or in a in a in in a any kind
00:21:26.159 --> 00:21:31.119
of a sound physicist has to encounter different
sound level multiple sound level. So, here
00:21:31.119 --> 00:21:36.480
we will discuss the how this two sound
level can be added together and in a logarithmic
00:21:36.480 --> 00:21:41.710
way. So, sound level 1 is having a level 1
L 1 dB. So, that can be translated to the
00:21:41.710 --> 00:21:49.369
I 1 as as you know there I reference by 10
to the power L 1 by 10, and there is a sound
00:21:49.369 --> 00:21:53.200
level 21 or sound source 2, which is available
L 2 and that is also give you a I mean very
00:21:53.200 --> 00:21:57.690
similarly I 2 equal to I reference into 10
to the power L by 10. L 2 by 10 and
00:21:57.690 --> 00:22:01.080
this sound intensity can be added arithmetically,
not the sound levels that is the decibel cannot
00:22:01.080 --> 00:22:04.760
be added the arithmetically .
So, suppose there is a 60 decibel and there
00:22:04.760 --> 00:22:12.679
is a 40 decibel you cannot add and say it
is a 100 decibel. You have to actually
00:22:12.679 --> 00:22:19.919
transferred the 60 decibel to the intensity
its the the respective intensity and the 42
00:22:19.919 --> 00:22:24.940
its respective and then you add the the the
intensity arithmetically and convert that
00:22:24.940 --> 00:22:29.289
intensity to the decibel.
So, here also I have to now add this arithmetically
00:22:29.289 --> 00:22:37.389
I 1 and I 2 and then this I 1 and I 2 gives
me the a new I total the new intensity, and
00:22:37.389 --> 00:22:44.470
then I will put it into that and finally,
the value will be like L the total intensity
00:22:44.470 --> 00:22:50.649
is this and the total level now you will
be or the final level will be now will be
00:22:50.649 --> 00:22:56.580
the this comes from the first part intensity
1 and this is comes from the second part intensity
00:22:56.580 --> 00:22:59.659
2 and if you provide in the I total by
I reference you will get the the total
00:22:59.659 --> 00:23:01.989
intensity .
Now addition of the sound level again let
00:23:01.989 --> 00:23:07.570
us further say that if this two levels L 1
and L 2 which we have just now discussed is
00:23:07.570 --> 00:23:14.450
similar. So, there are two sound source give
the similar output. So, L 1 is equal to L
00:23:14.450 --> 00:23:20.350
2 and that is equal to L. So, definitely that
the intensity of I 1 and I 2 also will be
00:23:20.350 --> 00:23:25.649
similar. So, the total intensity of the 2
y twice of I and finally, it will give instead
00:23:25.649 --> 00:23:31.239
of in in place of the total intensity is now
2 I by I reference now we can separate it
00:23:31.239 --> 00:23:37.179
out, one is the 10 log of I by I reference
plus 10 log of 2 . So, what is this? What
00:23:37.179 --> 00:23:44.279
is this 10 log of I by I reference it is nothing,
but the anyone of the level .
00:23:44.279 --> 00:23:50.789
So, this is the level which I am going to
add plus 10 log 2 is log 2 is 0.3m and 10
00:23:50.789 --> 00:23:58.090
log 2 is 3. So, if two sound source of equal
in nature equal output equal decibel level
00:23:58.090 --> 00:24:05.090
is added, suppose 30 and 30 is added. So,
the resultant will be 30 plus 3 33. So, that
00:24:05.090 --> 00:24:13.070
its what tells about .
So, next we will see the sound the the
00:24:13.070 --> 00:24:17.289
addition of the sound, addition of the sound
also can be infer from this particular graph,
00:24:17.289 --> 00:24:21.229
but how to read the graph. This in the x axis
it is the difference between the sound level
00:24:21.229 --> 00:24:27.889
is given and the y axis the addition will
the at to the sound sources it is also
00:24:27.889 --> 00:24:32.149
given .
So, let us go to the a small problem, where
00:24:32.149 --> 00:24:38.960
I am adding a 60 decibel sound to the 65.
So, by virtue of this particular expression,
00:24:38.960 --> 00:24:46.660
I got 66.2. Another example I get 90 and 95
and I express that in the mathematical form
00:24:46.660 --> 00:24:53.470
and I am getting 96.2 I am getting taking
the help of the previous equation. Now what
00:24:53.470 --> 00:24:59.210
I see is that in the both the case it is a
similarity what is this similarity? 62.2 66.2
00:24:59.210 --> 00:25:02.769
is nothing, but 65 plus 1.2 what is 65? 65
is the out of this is the higher one 60 and
00:25:02.769 --> 00:25:06.350
65 the higher one is 65.
So, 65 plus 1.2 and what is this? six 96.2
00:25:06.350 --> 00:25:10.940
is 95 plus 1.2. 95 is what the higher of this
two. So, if the difference between the two
00:25:10.940 --> 00:25:16.830
level of sound is 5 dB add 1.2 dB for the
largest sound that is actually translated
00:25:16.830 --> 00:25:18.830
over here.
Suppose the difference between the two level
00:25:18.830 --> 00:25:27.080
of sound is 5 dB of my I mean previous example,
you go from the x axis to here and then you
00:25:27.080 --> 00:25:33.440
go here. So, add 1.2 one point this is one,
this is 1.25. So, 1.2 to the larger sound
00:25:33.440 --> 00:25:43.489
. So, if there are two sound which are equal
in nature. So, there is no difference. So,
00:25:43.489 --> 00:25:49.869
the higher and lower there is no difference.
So, difference is 0.
00:25:49.869 --> 00:26:01.100
So, you have to add sorry you have to add
3 dB 3dB with that that we have already discussed
00:26:01.100 --> 00:28:00.749
in the
00:28:00.749 --> 00:29:20.559
previous
to previous slide. And if there are n number
00:29:20.559 --> 00:29:26.869
of sound sources suppose it is not to two
there are more more more L 1 2 3 4 more, then
00:29:26.869 --> 00:29:32.690
we can just rewrite this particular equation
in a this way and finally, which is summation
00:29:32.690 --> 00:29:38.190
sin, we can find out the what is the total
logarithmic or total logarithmic and finally,
00:29:38.190 --> 00:29:43.899
multiply by the that into 10 to the the L
total or the level total level .
00:29:43.899 --> 00:29:51.990
So, at the end of this this particular
lecture number 4, let us have some homework
00:29:51.990 --> 00:29:55.279
for you.
The first one is that the the intensity of
00:29:55.279 --> 00:30:02.519
the sound if it is 0.004 watt per meter square
and suppose another sound is of the sound
00:30:02.519 --> 00:30:09.619
pressure of 1.2 mega pascal, can you can you
find out the related sound levels. These
00:30:09.619 --> 00:30:13.889
two are not equal, but we have to find out
for one also, we have to find out for the
00:30:13.889 --> 00:30:20.750
second one also . So, just go to the previous
slides find out the how to convert and while
00:30:20.750 --> 00:30:26.200
converting in have to remember one thing,
that is when it is intensity and when it is
00:30:26.200 --> 00:30:29.889
power.
So, it is 10 log and when it is pressure it
00:30:29.889 --> 00:30:38.309
is 20 log and it is the the intensity, which
I am going to take for finding the level divided
00:30:38.309 --> 00:30:45.279
by the the the threshold that is for pressure
it is 2 into 10 to the power minus 5, for
00:30:45.279 --> 00:30:49.369
intensity it is or the this thing it is 10
to the minus 12 .
00:30:49.369 --> 00:30:55.350
Ah There is a second homework also, suppose
I have two different sound levels from two
00:30:55.350 --> 00:31:02.530
different source one is 58 dB and one is 62
dB . So, if they are added. So, what could
00:31:02.530 --> 00:31:08.029
be the resultant sound level? So, you have
to do the this thing by mathematical computation
00:31:08.029 --> 00:31:14.840
with the mathematical the formula, do it by
mathematically and then check your result
00:31:14.840 --> 00:31:21.440
from the graph, that the graph we have
discussed from the graph and finally, match
00:31:21.440 --> 00:31:26.159
your result.
There are some bibliography, there are
00:31:26.159 --> 00:31:31.739
some books has to be referred for this particular
lecture and those are the books you can
00:31:31.739 --> 00:31:40.019
find it in the library or maybe we can go
to the some library and get some books
00:31:40.019 --> 00:31:47.749
are available in E format also. So, thank
you for joining in this lecture number
00:31:47.749 --> 00:31:52.769
4, in the next lecture we will go to the the
that will be thus the last part of our
00:31:52.769 --> 00:31:58.179
acoustical physics and we will discuss something
and on the the near and far field propagation
00:31:58.179 --> 00:32:00.849
and also the loudness.
Thank you .