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Hi, welcome to another set of lectures. This time we will be talking a little more about sound in terms of some of the other
interesting descriptions and facts that we have not quite dealt with yet. Namely, we are going to talk about intensity
which has to do with volume and amplitude which we seem to have not talked about very much
and we will move into the doppler effect which
is actually very prevalent not only with sound, but with other types of waves as well, but we will demonstrate the principle using sound
so the first thing we are going to discuss is the
question of what determines how loud a sound is, the volume of the sound
we've talked about how that probably depends on the amplitude of the pressure sound wave, but
what is actually more important is the power that comes through, so we actually need to use power
and as you remember, power is related to the amplitude by the amplitude square
what is actually the thing that matters, it's not even power
it's intensity
intensity
which is ...
what area are we talking about and why does this come about?
let's consider we have an ear on this side
and then over here you have your friend
who has a pretty big mouth
your friend is speaking to you over here
you'll notice that if you're further away from your friend
he doesn't sound that loud, but then as you get closer and closer, he sounds louder and louder
so what's happening here
your friend is speaking with a certain power coming out of his lung, but then that power
as it goes away from his mouth, gets spread out
roughly speaking, you can look at this as part of a spherical wave
that we briefly looked at a couple assignments ago. As you get further away
chances are, your area goes up by r^2
it is getting spread more and more out, and for the same power spread over a bigger and bigger area
you'll see that
your ear intercepts less and less of the original power as you move away, so here you are getting pretty much all of it
back here you are getting about 50% and less and less and less, and that's why
you are going to
perceive the sound as quieter because you ear is [intercepting]
less power, even though the power at the source stays the same, everything gets spread out
another way to look is, if you consider
having, say, a tube
to constrict the sound from spreading
you also hear your friend a lot louder much further down the road, because the sound has not been allowed to spread
so that's why we have to consider the area
that the sound power is spread through
and that's why after we normalize, we get this thing called the intensity
which is measured, of course, SI unit, W/m^2, and that's intensity
as it turns out, however, our ear is a really amazing thing
it can perceive intensity all the way down from
...
all the way up to
...
before we feel pain
so having this massive range, this is 13 factors of magnitude, 13, that's 1 with 13 zeros behind it
that's 10 trillion (10,000,000,000,000) times difference, so it's usually not as useful to talk about in terms of
W/m^2, but rather, we use a log scale
and that's the decibel scale
and the decibel with defined with the following formula
some kind of loudness
in decibel
...
...
whatever intensity you have divided by this
I_o, and this I_o is the
smallest I perceptible by human ear
and that is what we briefly talked about, we are going to use 10^-12 W/m^2
so looking more closely at the formula
it's somewhat intuitive. It's basically saying for every 10 times increase
of the sound intensity, we are going to add 10 in our decibel scale
so that's every 10 times increase is add 10
so every step of 10 is 10 times increase
to get a handle on the decibel scale, I would perhaps suggest going to wikipedia and look up
"sound power", you'll find there
a good list of various sounds at different decibels
but I just want to note that our ear and our brain also work quite naturally on this logarithmic scale, because we do have
this big range, 10 trillion times, 13 factors of magnitude range of intensity
so
it's funny to think that our brain is actually very good at doing logarithm, which for some reason we don't learn until grade 12
in either case, so for example, if we have say, a refrigerator
or a dishwasher
those are roughly at 40 dB
but then you have your alarm clock
that's at about 80 dB
well you kind of feel that maybe from 40 to 80 that the alarm clock is twice as loud as the refridgerator
Not too much of a stretch
maybe even 5 or 10 times
but really, when you do the math
because it is a log scale, every 10 in the log scale is 10 times bigger
so ΔL is 40 dB
so therefore for every step of 10 we have to multiply by 10, this is
...
10^4, it's 10000 times more intense for the alarm clock but we only feel it as twice
so that just goes to show that our brain and our ear also work more or less with the logarithmic scale
now that we've seen how it is useful, let's do a couple numerical examples