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And again you know these waves which propagate in the water...
tsunami literally means in Japanese, harbor waves
because, you know, when they break on the coast, they rise up to a great height and submerge. This is what they do.
So they are known as "harbor waves". Tsunami in Japanese means "harbor waves".
So the height of the tsunami and all that can be estimated.
Here you know again, the propagation of the waves also.
There are gravity waves and capillary waves.
For any, for example, body of water
say if I have a perturbation...
Now, I know, suppose I throw a pebble on a pond, I'll get ripples.
So essentially these are capillary waves.
The surface tension on the water causes these surface waves to propagate.
The deeper waves, suppose I got a bigger perturbation, suppose I drop a rock, have an explosion under water or some other thing
then, gravity waves will be created
because of the mass of the water removed
you know, there is buoyancy, and
there is a column of water denser than the surrounding, so there will be a push
So the formula for the frequency of the waves...
this depends on the wave number,
the inverse of the wavelength
for gravity waves...
g is the acceleration due to gravity. omega squared equals to gk
and then, we essentially also have the capillary waves
the general formula for this is...
So the surface tension is also involved. Gamma is the surface tension
And rho is the density of the liquid
And there's a k cubed also.
This is the general expression
So this is the combination of gravity waves and capillary waves.
So you see now, that, what happens, there is a transition
depending on the
acceleration due to gravity, the density and the surface tension
there can be a transition from one to another
So the gravity waves are the one, the tsunami is nothing but a gravity wave.
They propagate through long distances
and the velocity of the waves depends on the wave number.
Actually the velocity goes something like v squared is equal to gk
Sorry it's the height of the wave. v squared equals to gh.
h is the height of the wave.
So, you can see now that
waves that move with a higher velocity are also submerged to a greater depth
or we can use d for the depth of the wave
so actually essentially it is one over k
k is our wave number
wavelength is lambda, so it is one over k
So you can see there is a transition for some k
corresponding to some wavelength
depending on the density and on the surface tension
So actually you can see for what value the two will match
and one will go into the other
So you see from this that for larger values of k
these capillary waves will dominate
and for longer wavelengths
the gravity wave will dominate.
So that's why the tsunami wave can be quite high
and they move at high velocities
And actually you can match this with the energy of the...
for example, we heard that the velocity of the tsunami was something like 500 km/hr.
Right? About a jet liner. Or maybe 1000 km/hr.
So how do we get such high velocities? So you know the energy released
in this quake is about 10^20 Joules.
So quite a substantial part of this could be transmitted to the water
causing the wave motion.
So, you can roughly estimate the thing like this...
We saw that the area involved was something like...
something like 1000 km^2
1000km x 1000km. This was roughly the area of the water.
So roughly one million kilometer square.
So we can calculate roughly the kinetic energy of the water
So the depth is about, you can say
100 m. This is also deduced from the
epicenter where the earthquake took place
So they realize this much of the plate was broken off
The fault line.
So you can see how much volume this covers
So it works out to roughly about 10^18 cc (cubic centimeters)
or you want in liters, its 10^15 liters or 10^12 cubic meters.
So you know the mass of the water
And now you can work out the velocity
The velocity involved in this.
So, you roughly have M(v^2) of the order of 10^20 Joules.
If you do this calculation you will get a v of about,
close to what they said,
1000 km/hr.
So this gives an idea of how these things operate.
Of course for high values of k there will be a surface wave, at small wavelengths.
And the transition is interesting to work out.
For example, if you know for water the surface tension...
surface tension of water is about 70 dynes per centimeter
and density one gram per cc
So you work out for water, the transition wavelength or the transition frequency
It works out to a few Hertz
About 12 Hertz or something like that...
ten Hertz or something.
So for smaller frequencies or longer wavelengths
the gravity wave will dominate
and for smaller wavelength and larger k, the capillary wave will dominate
So you can see the transition
So in this case clearly the surface waves are not important
its the depth, its the deeper gravity waves which are important
So your gk is important
So you can estimate the velocity of the waves in this fashion
So this is one way. And you can calculate the potential energy. How much is heaped up.
So much of water being heaped up, you can calculate the potential energy.
So that also matches with this. This is just to give you a rough idea.
The numbers involved.
And suppose, if you have a different planet (satellite), like Titan. Titan is supposed to have oceans of liquid methane.
Suppose now a similar thing happens there.
You can calculate for that particular fluid
what is the surface tension
See, instead of water suppose you have alcohol.
The surface tension is much lower, say, around twenty.
Whereas the density of the order of, comparable to 0.8.
So again the crossover frequency one can work out
So if you know that the particular planet is covered with oceans of some methane or whatever
or ammonia, you can again do the...
And of course it depends on g. So suppose you have got
one of the findings of the Cassini spacecraft is
that Titan has got weather similar to the Earth.
But running on the methane cycle, liquid methane cycle.
Probably some nitrogen is also there, liquid nitrogen.
So the surface gravity on Titan is quite small compared to the Earth.
Again you know the frequency of the waves and everything would get affected.
Or given a wave of particular frequency, the velocity would be different
Small. The velocity will be smaller. Propagation times will be longer.
Or if you take another example. Europa is one of the satellites of Jupiter.
They think there may be a lot of water below the surface.
That's why, some spacecraft they are launching to exclusively monitor the satellite Europa.
So suppose this has also got a huge ocean underneath the surface.
So if it is subject to all these kind of wave phenomena
But for Europa, surface gravity is only one-seventh of the Earth.
So you see any velocity of any of these waves will be much less.
So it is easy to deduce many things from all these things
So it all follows from...
So I gave you some idea about how to estimate for earthquakes. This is the energy.
So next time you read some earthquake was there
of Richter seven or nine or whatever
you can plug in the formula and you can see how much energy is released
And since its a logarithmic scale, Richter one will correspond to hardly twenty Joules.
In fact if I drop this duster on the floor, its just about Richter one [sound of duster hitting the floor]
So, logarithmic scale. Magnitudes.
Magnitude thirty doesn't seem very different from magnitude one
but that's the classical limit of the Hubble telescope.
So its a trillion times fainter than what you do here.