CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and...

25
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

Transcript of CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and...

Page 1: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same

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

Page 2: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
andres
Text Box
andres
Text Box
CASE-1 Waves travelling in the same direction
andres
Text Box
CASE-1A Interference between two harmonic waves of the same frequency w (therefore, the same k) but different phase
andres
Text Box
Df
andres
Text Box
Dx
andres
Text Box
Df = k Dx
andres
Rectangle
andres
Text Box
Interference of travelling waves
andres
Rectangle
andres
Stamp
andres
Text Box
Interference (synonymous of addition of waves)
andres
Text Box
Page 3: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
andres
Text Box
andres
Text Box
andres
Text Box
andres
Text Box
andres
Text Box
andres
Text Box
andres
Text Box
andres
Text Box
andres
Rectangle
andres
Text Box
andres
Text Box
Interference factor
andres
Stamp
Page 4: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
andres
Stamp
andres
Stamp
andres
Text Box
andres
Stamp
andres
Stamp
andres
Text Box
Same phase
andres
Text Box
Peaks and valleys coincide
andres
Text Box
andres
Text Box
Example: Full constructive interference case ( f = 0 )
andres
Text Box
Page 5: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
andres
Stamp
andres
Stamp
andres
Stamp
andres
Text Box
andres
Stamp
andres
Text Box
different phase
andres
Text Box
Particular case: Dx =l/2
andres
Polygonal Line
andres
Text Box
Example: Destructive interference case ( f = p )
andres
Text Box
andres
Text Box
andres
Text Box
andres
Text Box
andres
Text Box
andres
Line
andres
Line
andres
Line
Page 6: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
andres
Stamp
andres
Line
andres
Line
andres
Text Box
andres
Text Box
andres
Text Box
andres
Text Box
andres
Line
andres
Line
andres
Line
andres
Line
andres
Line
andres
Line
andres
Line
andres
Line
andres
Rectangle
andres
Rectangle
andres
Text Box
andres
Text Box
andres
Line
andres
Line
andres
Line
andres
Text Box
Dx
andres
Text Box
(2)
andres
Text Box
(1)
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Line
andres
Text Box
Dx
andres
Text Box
P
andres
Text Box
Q
andres
Text Box
B
andres
Text Box
andres
Text Box
andres
Text Box
P and Q are in phase
andres
Text Box
A and B are out of phase by (k) (2 Dx)
andres
Text Box
andres
Text Box
andres
Line
andres
Text Box
A
andres
Text Box
andres
Text Box
andres
Line
andres
Text Box
andres
Text Box
Example: Controlling the degree of interference ( 0 < f < 2p )
andres
Text Box
Mirror
andres
Text Box
Mirror
andres
Text Box
andres
Line
andres
Text Box
andres
Line
andres
Text Box
andres
Text Box
andres
Line
andres
Line
andres
Line
andres
Line
andres
Stamp
andres
Text Box
andres
Text Box
Page 7: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Line
andres
Line
andres
Text Box
Dx
andres
Text Box
Dx
andres
Line
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Text Box
Before the reflection
andres
Text Box
After the reflection
andres
Oval
andres
Text Box
andres
Text Box
draw
andres
Text Box
Lens
andres
Text Box
andres
Text Box
andres
Text Box
andres
Text Box
FIGURE-1
andres
Text Box
FIGURE-2
andres
Oval
andres
Text Box
andres
Line
andres
Text Box
andres
Text Box
andres
Line
andres
Oval
andres
Line
andres
Oval
andres
Line
andres
Text Box
andres
Text Box
andres
Text Box
A
andres
Text Box
B
andres
Text Box
B
andres
Text Box
A
andres
Oval
andres
Oval
andres
Text Box
Page 8: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
andres
Text Box
andres
Text Box
andres
Text Box
andres
Text Box
Page 9: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
andres
Text Box
andres
Text Box
Page 10: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
andres
Text Box
CASE-1B Interference between waves of slightly different frequency (This case will be done in Chapter 17)
andres
Text Box
CASE-1C Coherent waves
andres
Rectangle
andres
Rectangle
Page 11: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
andres
Text Box
andres
Text Box
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Text Box
CASE-2 Waves travelling in the opposite directions
andres
Text Box
Standing Waves
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Rectangle
Page 12: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Text Box
and this is what happens:
Page 13: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
andres
Text Box
f1
andres
Text Box
f2
andres
Text Box
f3
andres
Text Box
f4
andres
Text Box
f5
andres
Text Box
Fig. Solutions obtained by intuition
andres
Rectangle
andres
Text Box
Resonance of waves in a string
andres
Text Box
Case 2A String fixed at one end
andres
Text Box
Intuitive solutions
Page 14: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
andres
Text Box
For the case when one end of the string is fixed
andres
Text Box
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Rectangle
Page 15: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
andres
Rectangle
andres
Rectangle
andres
Rectangle
Page 16: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
andres
Text Box
andres
Text Box
...
andres
Rectangle
andres
Rectangle
andres
Text Box
Analytical solution
andres
Text Box
General solution.
andres
Text Box
But we have to impose the particular boundary conditions of the problem (i.e. that the string is fixed at one end)
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Rectangle
andres
Rectangle
Page 17: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
andres
Text Box
satisfy
andres
Rectangle
andres
Rectangle
Page 18: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
andres
Text Box
L
andres
Rectangle
andres
Text Box
Case 2B String fixed at both ends
andres
Text Box
Intuitive solutions
andres
Rectangle
andres
Rectangle
Page 19: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
andres
Rectangle
andres
Text Box
Analytical solution
Page 20: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
andres
Rectangle
andres
Rectangle
Page 21: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
andres
Rectangle
andres
Line
andres
Line
andres
Rectangle
andres
Rectangle
andres
Polygonal Line
andres
Rectangle
andres
Rectangle
andres
Oval
Page 22: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
andres
Text Box
andres
Text Box
This is a generalization of the example (to be worked out in the next page) for the case of having jut two particles
andres
Text Box
andres
Text Box
Page 23: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
Page 24: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
Page 25: CHAPTER 16: WAVES-1 16.2. Interference · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves Case 1 Waves travelling in the same
andres
Text Box

4 Waves (2.4.3 Interference - Part A) G482 Electricity, Waves & Photons 4 Waves (2.4.3 Interference - Part A) G482 Electricity, Waves & Photons 2.4.1 Wave.

4 Waves (2.4.3 Interference - Part A) G482 Electricity, Waves & Photons 4 Waves (2.4.3 Interference - Part A) G482 Electricity, Waves & Photons 2.4.1 Wave.

Interference of Light Waves - Wake Forest Student, …users.wfu.edu/ucerkb/Phy114/L15-Interference.pdfInterference of Light Waves Conditions for interference Young’s double slit

Interference of Light Waves - Wake Forest Student, …users.wfu.edu/ucerkb/Phy114/L15-Interference.pdfInterference of Light Waves Conditions for interference Young’s double slit

Electromagnetic Waves Interference 3 Coherence

Electromagnetic Waves Interference 3 Coherence

INTERFERENCE OF WAVES Section 9.1. Key Terms Interference Principle of Superposition Constructive Interference Destructive Interference.

INTERFERENCE OF WAVES Section 9.1. Key Terms Interference Principle of Superposition Constructive Interference Destructive Interference.

Interference in sound waves

Interference in sound waves

Waves Longitudinal and Transverse Waves Transverse Waves on Strings Periodic Waves Reflection and Refraction of Waves Interference and Diffraction Standing.

Waves Longitudinal and Transverse Waves Transverse Waves on Strings Periodic Waves Reflection and Refraction of Waves Interference and Diffraction Standing.

PHY138 – Waves, Lecture 6 Today’s overview Constructive and Destructive Interference Interference Patterns Beats.

PHY138 – Waves, Lecture 6 Today’s overview Constructive and Destructive Interference Interference Patterns Beats.

CHAPTER 16: WAVES-1 16.2. Interference€¦ · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves ... Case 2A String attached at

CHAPTER 16: WAVES-1 16.2. Interference€¦ · CHAPTER 16: WAVES-1 16.2. Interference standing waves and resonance Interference of travelling waves ... Case 2A String attached at

Superposition of waves and interference

Superposition of waves and interference

Lecture 38 Review of waves Interference Standing waves on a string.

Lecture 38 Review of waves Interference Standing waves on a string.

Interference Interference of Waves When waves ______ at the same place at the same time, ________________ occurs.

Interference Interference of Waves When waves ______ at the same place at the same time, ________________ occurs.

Chapter 17 Waves (II) Sound Waves. Supersonic Speeds, Shock Waves Sound Waves Speed of Sound Pressure Fluctuation in Sound Waves Interference Intensity.

Chapter 17 Waves (II) Sound Waves. Supersonic Speeds, Shock Waves Sound Waves Speed of Sound Pressure Fluctuation in Sound Waves Interference Intensity.

2.1.1_slides Plane Waves and Interference

2.1.1_slides Plane Waves and Interference

Interference of Waves Beats Double Slit

Interference of Waves Beats Double Slit

1.5 Interference of Waves

1.5 Interference of Waves

5.1.4 Interference, Standing Waves, and Resonance

5.1.4 Interference, Standing Waves, and Resonance

OptiXplorer - Michigan State University...4 Scalar theory of light waves and diffraction — Fourier optics 20 4.1 Plane waves and interference 20 4.1.1 Interference of plane waves

OptiXplorer - Michigan State University...4 Scalar theory of light waves and diffraction — Fourier optics 20 4.1 Plane waves and interference 20 4.1.1 Interference of plane waves

Electromagnetic Waves & Interference of light

Electromagnetic Waves & Interference of light

Interactions of Waves. Reflection Diffraction Refraction Destructive interference Constructive interference.

Interactions of Waves. Reflection Diffraction Refraction Destructive interference Constructive interference.

Chapter 16 The Dynamic Ocean. Section 16.2 Waves & Tides.

Chapter 16 The Dynamic Ocean. Section 16.2 Waves & Tides.