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We will begin our discussion on waves and first talk of transverse and then longitudinal waves.
the medium has particles over here; without the particles of the medium actually traveling between the two points.
Lets look at this statement a little more in detail.
Ok. Now just tell me something- say you are standing here and your friend is standing here
now as you shout out to your friend
sound waves carry energy of your voice from A to B.
suppose you jerk this end of a string. Let me just draw this.
You can actually watch waves travel as you shake one end of a stretched string, up and down. You would be moving your hand in this direction.
and these waves that are created move towards the other end.
Now these waves carry energy from A
to a point B.
now just notice something important in these two examples
see energy travels from A to B
but do the particles of the medium also go from A to B?
does the string over here after some time reach this point or does the air that is present at A after some time reach point B?
Think about this a little!
Both these are examples are of mechanical waves-
by mechanical waves we mean waves that require a material medium to travel.
we said that only energy is transferred from one point to the other but the particles
that were at A do not move and reach B after some time
Does this mean that the particles of the medium do not move at all?
no that's not the case
The first one is a longitudinal wave and sound wave travels as a longitudional wave.
and waves along the string travel as transverse waves. Now
what is the difference between a longitudinal wave and a transverse wave
in this case the vibrations of the particles of the medium
the particles of the medium are vibrating in this direction. The vibrations of the particles of the medium is same as the direction of travel of the wave.
The arrow that I have drawn here shows the direction of
travel of the wave.
and the direction of the particles of the medium
is also in the same direction- the direction of
motion of the particles of the medium
whereas if you look at a transverse wave
the direction in which the wave travels is the same
but the particles of the medium are moving in a direction perpendicular to the direction of
travel of the wave.
So this is the direction of travel and this is the direction of
motion of the particles
so you can see in case of longitudinal waves the direction of travel and motion of particles in the same
and sound waves are a typical example of
longitudinal waves
in case of transverse waves the direction of travel and motion of the particles is perpendicular to each other and a typical example of a transverse wave
can be waves in a stretched string
or electromagnetic waves.
See in case of em waves there are no particles that vibrate.
but we have an electric field and a magnetic field that are perpendicular to the direction of travel of the wave.
Say this is the electric field this is the magnetic field and this is the direction in which the wave travels.
all our discussion will hold true for electromagnetic waves also but we will be talking about the particles of the medium so we will be talking about
mechanical waves because it's easier to understand
the description in terms of mechanical waves.
now let's look at transverse waves a little more in detail.
the perpendicular ones
OK now you know what the movement of these particles reminds me of?
Say you are standing in a stadium and watching a cricket match or let's say a concert and let's say you are standing here or sitting here and you have your friend here
and there are a lot of people in the stadium
and then you want to really cheer the players and the crowd makes a wave
so what happens - to make the wave, when its your turn, you stand up and then you sit down again
now your friend whose a short distance away, let's say the wave is travelling in this direction
your friend whose a short distance away does the same after a short while- he stands up and then he sits down. You don't have to run in the stadium.
you have to remain in your seat, you have to remain in the same position but you have to stand and sit when the wave passes you.
now each particle in the medium seems to be doing the same
they are also playing the same game.
see the particles can't think like you, you can't tell them to move so they move only when they experience a force
So when the particles experience a force exerted by adjacent portions of the medium. for instance in the stretched string when it moves lets say
upwards it also pulls the
adjacent portion of the string also in the upward direction.
The force is due to the tension. If there is no tension in the string, if the string is slack, in that case there will be no movement, the wave will not propagate.
Let us write an expression for the velocity of the waves. This expression is v =
frequency times the wavelength. Lets see how do we arrive at this relation.
See if you notice there is something interesting happening over here
the frequency with which the particles of the medium are vibrating
is the same as the frequency of the source that produces these waves.
let's say the frequency with which the source moves is f so the frequency with which
each point on the wave or each point in the medium moves is also f
in that case we say that the frequency of the wave is f.
now when the source vibrates once
then the wave form moves forward through a distance which is the wavelength lambda
so if the source vibrates once the wave moves forward through a distance lambda, now if the source vibrates
f times the wave moves forward through a distance lambda times the frequency
now this means the wave moves forward through a distance of lambda times f in one second
so you can say the velocity of the wave
velocity is distance/time; in this case distance is lambda times f and the time is 1 second
so in this case the velocity of the wave becomes lambda times the frequency of the wave.
Now lets take a look at longitudinal waves
I will draw particles to show how longitudinal waves propagate. Let us just draw this..
maybe you can also draw this along with me it will give you a better understanding
we are talking of longitudinal waves like sound waves.
I have drawn a grid over here and I'll mark particles at equal distances. This is a rarefaction, R then you have a compression, C here.
see at a compression the particles are pushed together
at a rarefaction the particles move away from each other
so alternately we have a compression and a rarefaction
see in a compression the particles are being pushed towards this point
so lets say we have a few points over here and the particles are being pushed towards the centre of the compression
OK now in case of a rarefaction say we have a particle over here then this particle is being pushed away, which means the particle is moving in this direction.
it is going towards the right away from the rarefaction.
again if you look at the rarefaction here the particles have moved away from it
maybe we can draw another particle over here. That particle will move away from the rarefaction.
we have a particle on this side, that is also moving away from it which means it is moving towards the compression.
once again
particles are moving towards the compression
so you have particles that will be close together at the compression and particles are moving away from the
rarefaction.
now we want to do draw a wave to denote this so what we are going to assume is this - if particles move in this direction we denote that above the axis
in a positive direction and and if the particles move in the opposite direction we take that as negative so we show that below the axis.
you can see that the particles are not moving at the centres of the compression and rarefactions
so here they have zero displacement of the moving towards the
right
in this region the particles are moving towards the left
here again they are moving towards the right and moving towards the left
moving towards the right, moving towards the left. Ok now this the wave that we have drawn
and you can see that was a sine wave is representing a longitudinal wave.
though there is no motion in this direction
But still we are drawing a sine wave to represent the displacement of the particles
because their displacement in the horizontal direction is shown above and below the axis.
now after half a cycle we have a rarefaction that has moved here
now a compression at this point where we earlier had a rarefaction, a rarefaction here and a compression here
if it is a compression particles are moving towards the compression
in case of a rarefaction they move away.
as this is a negative displacement
this is say at time t=0. This is
half a cycle later and this is at a full cycle later so you can see that we are back to what we had at t=0.
you can also draw some intermediate states say at T/4 and 3T/4.
This graph that we have drawn shows the displacement
you could have also shown the pressure
if you draw a pressure vs x graph that would look like this.
see at the compression we would have a high pressure region
at a rarefaction we would have a low pressure region
again at the compression high pressure
at the rarefaction low pressure and notice that this is normal pressure
you don't have positive and negative pressure
you have this is normal atmospheric pressure, above atmospheric pressure and below atmospheric pressure
since the molecules are close here the pressure is high and since the molecules are far apart the pressure is low
and this will again be a low pressure region. So you get a graph
which looks like this