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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
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
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
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
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]
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)
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
Activity
a)Sketch the resultant wave of the following waves
b) Is it constructive or destructive interference?
c)Calculate the resultant amplitude
Question 1
Question 2
Answers Question 1
Answers Question 1
b) Constructive
c) 40m
Answers Question 2
Answers Question 2
b) Destructive
c) 5m

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Lo 5 rosalie ho

  • 1.
  • 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
  • 13. Answers Question 1 b) Constructive c) 40m
  • 15. Answers Question 2 b) Destructive c) 5m