Superposition of Waves Video Lecture - Physics Class 11 - NEET

the principle of superposition of waves
according to the principle overlapping
waves add algebraically to produce a
resultant wave or net wave in other
words when any number of waves met
simultaneously at a point in a medium
the net displacement at a given time is
the algebraic sum of the displacements
due to each wave at that time for
example let us consider two vanes
traveling together along the same
stretch string in opposite directions
they met and pass through each other and
move on
independently as shown in Figure
each picture depicts the resultant
waveform in the stream at a given
instant of time the principle of
superposition of waves imply that the
overlapping waves do not in any way
alter the travel of each other in
mathematical form suppose y1 of X D and
y2 of X D are the displacements that any
element of the string would undergo if
each wave travelled along when the two
waves overlap the displacement Y of X D
of one element of the string would be
given by Y X T equals to y1 of X T plus
y2 of X D in general it is a wave
functions of the moving waves 1 y1
equals to F 1 into X minus V T y2 equals
to F 2 into X minus V T and so on Y n
equals to F n into X minus V T then the
wave function describing the resultant
disturbance in the medium is y equals to
Y 1 plus y 2 plus so on plus y N equals
to F 1 into X minus V T plus F 2 into X
minus V T plus so on plus F n into X
minus V T equals to Sigma I equals to
1/2
and of Fi into X minus VT to illustrate
the principle let us consider two ways
of same angular frequency W equals 2 of
2 pi by T same angular wave number K
equals to 2 pi by lambda same amplitude
a traveling with the same speed along
the positive direction of x axis if the
two waves one out of phase by a constant
angle q their equations can be written
as Y 1 of XT equals to R sine of Omega t
minus KX y 2 of XT equals to R sine of
Omega t minus KX plus Phi