2. 14-9 Superposition of waves
Have you ever wondered how you can identify the
different instruments playing in a concert at the same
time ?
This is because of the Principle of
Superposition of Waves
3. Principle of Superposition of
Waves
The net force at a point= sum of all forces
Resultant displacement of the point=sum of
displacement (+/-) of all the waves at that point
Waves don’t affect other waves’ interaction with the
medium
Waves passes through each other unaffected
4. Terms
Resultant Wave
Wave obtained by adding all the component
waves
Superposition
Process of adding waves to produce a wave
that is the sum of all waves
Interference
2 or more waves combining to produce a
resultant wave
5. 14-10 Interference of Waves
Travelling in the Same direction
There are 2 waves
Wave 1 has a phase constant of 0 and wave 2 has a
phase constant of Φ
The different of the phases is Φ-0=Φ
6. Wave functions of given 2
waves
Wave function 1 :D1(x,t)= Asin(kx-ωt)
Wave function 2 :D2(x,t)=Asin(kt-ωt+Φ)
Or
Wave function2:D2(x,t)=Asin[k(x+Φ/k)-ωt]
7. Resultant wave
Eqn of resultant wave of wave 1 & 2:
D(x,t)=2Acos(Φ/2)sin(kx-ωt+Φ/2)
Resultant amplitude of resultant wave
from wave 1 & 2 = 2Acos(Φ/2)
8. Constructive and destructive
interference
Constructive : When the phase difference of 2 waves
are in a multiple of 2pi rad
Destructive: when the phase difference of 2 waves
are in a multiple of pi rad , they will cancel each other
out
9. Activity
a)Sketch the resultant wave of the following waves
b) Is it constructive or destructive interference?
c)Calculate the resultant amplitude