CHAPTER 16: WAVES-1 16.2. Interference€¦ · CHAPTER 16: WAVES-1 16.2. Interference standing...
Transcript of CHAPTER 16: WAVES-1 16.2. Interference€¦ · CHAPTER 16: WAVES-1 16.2. Interference standing...
A. La Rosa Lecture Notes
PH-213 GENERAL PHYSICS ________________________________________________________________________
CHAPTER 16: WAVES-1 16.2. Interference
standing waves and resonance Interference of travelling waves
Case 1 Waves travelling in the same direction Case 1A Interference between waves of the same
frequency Case 1B Interference between waves of slightly different
frequency (This case will be done in Chapter 17) Case 1C Coherent waves
Case 2 Waves travelling in opposite direction Standing waves Resonance of waves in a string
Case 2A String attached at one end Intuitive solutions, analytical solutions Case 2B String attached at both ends Intuitive solutions, analytical solutions
CASE-1 Waves travelling in the same directionCASE-1A Interference between two harmonic waves of the same frequency w (therefore, the same k) but different phase
Δφ
Δx Δφ = k Δx
Interference of travelling waves
Interference (synonymous of addition of waves)
Interference
factor
Same phase
Peaks and valleys coincide
Example: Full constructive interference case ( φ = 0 )
different
phase
Particular case: Δx =λ/2
Example: Destructive interference case ( φ = π )
Δx
(2)
(1)
Δx
P
Q
B
P and Q are in phase
A and B are out of phase by (k) (2 Δx)
A
Example: Controlling the degree of interference ( 0 < φ < 2π )
Mirror
Mirror
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Δx
Δx
Before the reflection
After the reflection
draw
Lens
FIGURE-1
FIGURE-2
A
B
B
A
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CASE-1B Interference between waves of slightly different frequency (This case will be done in Chapter 17)
CASE-1C Coherent waves
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CASE-2 Waves travelling in the opposite directions
Standing Waves
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and this is what happens:
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f1
f2
f3
f4
f5
Fig. Solutions obtained by intuition
Resonance of waves in a string
Case 2A String fixed at one end
Intuitive solutions
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For the case when one end of the string is fixed
2
2 2 2
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Analytical solution
General solution.But we have to impose the particular boundary conditions of the problem (i.e. that the string is fixed at one end)
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satisfy
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Case 2B String fixed at both ends
Intuitive solutions
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Analytical solution
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This is a generalization of the example (to be worked out in the next page) for the case of having jut two particles
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