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is the phase difference between them. It is assumed that the waves are plane and move almost along a line. Thus, wave equations are
………..(i)
……….(ii)
Here,
When both the waves travel simultaneously, the resultant wave at
P
can be obtained by principle of superposition.
Let,
…………(iii)
and
………..(iv)
Squaring and adding Eqs. (iii) and (iv), we get
……….(v)
As
……….(vi)
Also
……..(vii)
The resultant wave becomes
….(viii)
Clearly the resultant wave has the same frequency and speed as the interfering waves
or
and
or
at those points where
or
or
and
or
at those points where
or
Now, the two waves from
S
1
and
S
2
meet at some point (say
P
). Then, according to principle of
superposition net displacement at
P
(from its mean position) at any time is given by
Here,
y
1
and
y
2
are the displacements of
P
due to two waves individually.
This gives
and
Where
is called the amplitude ratio. If
and
are intensities of two interfering waves, then
If
, then
In this case
and
