Standing, Stationary Waves - Waves Video Lecture - Class 11

hello friends this video on waves part
18 is brought to you by exam feel calm
no more fear from exam please make sure
that you have watched all the videos
till patch 17 before going ahead with
part 18 now that we have finished
discussing about travelling waves let us
focus on standing waves or stationary
waves now as the name suggests
stationary waves would mean something
which is at rest which is stationary and
not moving so what can stationary waves
be sounds interesting
right so let us have a look at this when
two waves of same frequency wavelength
and amplitude traveling in opposite
directions will interfere and produce a
standing wave so standing wave is
basically produced by two waves which
are traveling that means two traveling
waves can produce a standing wave now
what is the condition the condition is
that the two waves must be traveling in
opposite direction and they should be of
same frequency wavelength and amplitude
so let us have a look at this here we
have two traveling waves which are
traveling in opposite direction if you
see the wave on the top it is travelling
in this direction whereas the wave in
the below diagram is travelling towards
left
so both these waves are travelling in
traveling opposite to each other now if
you try to visualize this tsunami oh you
can see that at certain instances the
peak of the first wave will overlap with
the peak of the second wave therefore
what will happen both the peaks will add
up right to form the resultant wave
similarly at certain points if you see
the peak of the first wave combines with
the negative of the second wave thus at
certain points the net amplitude will
become zero so that is how I mean at
different instants of time sometimes
they both will together rise up
sometimes they both will together result
in a dip down so as a result you will
have a standing wave which will look
like this if you see once it goes up
then again it goes down again it goes up
and so on so what's happening here if
you look now you forget about the first
two wheels you just have a look at the
second thing when you look at the second
wave do you feel in any way that the
wave is traveling no right because as I
mentioned before also whenever we talk
about the displacement of the wave or
the movement of the wave form as a whole
what we observe is how the peaks of the
wave are moving if you see the first two
waves the peak seems to be moving
towards right in the second wave the
peak of the wave seems to be moving
toward left but if you look at this wave
you can very clearly see that the wave
is not at all moving either to the right
or to the left the wave is stationary so
that is why the speaks waves are
standing waves or stationary waves
because they do not travel to either
side they just be at their own position
so stationary waves waveform does not
move formed by two waves traveling in
opposite direction with same amplitude
same wavelength and same frequency now
let us look at the same concept
mathematical just now we discussed about
reflection of waves right so let us make
use of reflection here let us suppose
that you have a rigid wall let us
suppose that consider this first wave
and let us suppose that this wall which
you see here it is a rigid wall which
does not move so what did we study in
reflection we studied that when our wave
comes and hits a rigid wall what happens
it reflects back with a phase difference
of five right so this wave will start
going back so let us consider that this
first wave is our incident wave which is
hitting this rigid wall after reflection
is go it goes back towards left so let
us suppose that the second wave is
nothing but it is representing the
reflecting reflected wave now what
happens when the reflected wave travels
towards the left there is another
incident wave which is coming towards
the right because this coming and going
of the waves keep continuing right so if
you observe at any instant of time the
wave that is the reflected wave will
superpose with the incident wave because
the incident wave is continuously coming
from left towards right
so in incident wave is continuously
coming from left to right and now after
getting reflected the reflected wave
will keep continuing to travel from
right to left so at any instant of time
there will be two waves one going
towards right and the other going
towards left so these two waves will
overlap and form a standing wave right
so now let us look at it mathematically
let us suppose our incident wave for the
first wave which I am talking about Y 1
is equal to in sine KX minus Omega T I
am ignoring fine now let us say that the
second wave which is travelling towards
left is represented by a sine KX plus
Omega T y plus Omega T because the
second wave is travelling towards the
negative 8 x axis and I have already
told you that a travelling wave towards
negative x-axis is represented by KX
plus Omega T right so now when these two
waves will superimpose what will happen
you will get another wave which will be
represented by Y so that another wave
will be nothing but Y 1 plus y 2 so what
will be that wave let us look at this so
Y will be Y 1 plus y 2 so what is y 1 it
is a sine KX minus Omega T
and what is y2 it has a sine KX plus
Omega T so this can be written as a a
you take almond so you will have sine KX
minus Omega T plus sine KX plus Omega T
so again from your trigonometric
relations the quantity which you have in
the bracket is of the form sine a plus
sine B and sine a plus sine D is equal
to 2 sine a plus B by 2 cos a minus B by
2 so using this you can write a and this
becomes 2 sine a plus B so a plus B
becomes 2 KX by 2 cos a minus B so a
minus B becomes 2 Omega T by 2 so this
becomes 2 a sine KX cos Omega T so what
is this this represents the resultant
wave which is formed by superposition of
two waves in opposite direction with
same amplitude frequency and wavelength
now look at this wave is this a
traveling wave no it is not because a
traveling wave is in the form of a sine
KX minus Omega T but here you have a
sine function plus a cosine function so
this doesn't represent a travelling wave
this equation basically represents a
standing wave now which quantity in this
equation represents the amplitude of a
standing wave the amplitude is
represented by this quantity that is two
a sine KX therefore here we go an
interesting thing which we observe here
is the amplitude in case of a standing
wave is dependent on the position of the
particle
and it's because amplitude what is this
amplitude it is basically the maximum
displacement made by the particles of
the medium so in case of a traveling
wave the amplitude is same for all the
elements like right it is not dependent
on the position of the element but in
this case the amplitude is dependent on
position of the element of the medium so
this this quantity to a sine KX
represents the amplitude of your
standing wave and cos Omega T represents
the time dependence variation order
feels for the standing wave now if you
look at this diagram it basically shows
you how to traveling waves combine and
gives rise to a standing wave if you
observe this diagram the blue the wave
represented by the blue line represents
a standing wave so see the firth in the
first step the amplitude is maximum then
it reduces again it goes down and then
it goes to the maximum value of the
opposite direction so how does this
overlap takes place you can see it one
wave is represented by a dotted line and
the other ways a wave is represented by
a grayish line so these two waves
overlap in this way and then you get the
corresponding standing wave I mean I
found this diagram very convenient and
very easy to visualize the situation
because the waves as a chapter where I
cannot make you see everything there are
certain things which is beyond my
capacity to display for example how two
traveling waves are traveling in
opposite direction and forming a
standing wave right it is something
which you yourselves need to visualize I
can just help you to visualize it in the
correct way so I found that this diagram
is very suitable man and it is also
given there in your textbooks and I feel
that if you observed it very carefully
you can understand how do you get this
kind of a standing wave which doesn't
move on either side
only that it's amplitude keeps changing
so now that we have discussed about what
is a standing wave let us have a quick
discussion on a comparison between a
traveling wave and the stationary wave
standing wave is also non stationary
wave right in the same way as you have
another name for travelling wave that is
progress of wave
so let us quickly differentiate between
them when I talk of a travelling wave
the wave form moves movement of the wave
form is always indicated by the movement
of the P softer will if you observe the
peaks you see that they keep moving
towards right so that shows that the
wave form moves whereas in case of a
standing wave the peaks doesn't move
they seem to be at the same place so the
wave form is stationary wave amplitude
is same for all the elements here the
amplitude is denoted by a and this holds
true for all the elements of them wave
but in this case the amplitude is given
by the foreign setting to a sine KX so
the amplitude is dependent on X that is
the position of the particles so that is
also a major difference between
traveling wave and a stationary wave so
we represent the travelling wave by this
equation a sine KX minus Omega T plus
Phi
where is the amplitude and KX minus
Omega T plus Phi represents them phase
of the wave whereas in case of a
stationary wave we represent it as - a
sine KX cos Omega T where - is I its
represents the amplitude and cos Omega T
represents the time variation thank you
please visit exam few calm to watch free
educational videos try free online tests
get the best quality study materials
study from the best tutors and mentors
and much more thank you once again