Wave Phenomena

Wave Phenomena

Wu, JinyuanFermilabAug. 2013

Aug. 2013, Wu Jinyuan, Fermilab [email protected] Wave Phenomena 2

Introduction We will talk about classical physics only. We will try to show phenomena not commonly

seen in text book.

Many pictures in this file are taken via www.google.comThey are used for review and comments only.

http://www.google.com/

Oscillation of Things



Repetitive Motions of many Things

We live in a world with two type of motions: One pass motions. Repetitive motions.


Inertia and Recovery Force of Oscillations

An object needs two elements in order to oscillate: Recovery force: so that the object moves back and forth around an origin. Inertia: so that the object keeps moving.


Boundary Conditions and Eigen Values

When an object is supported differently, the resonant frequencies can different.

Different boundary conditions causes different movement modes with different Eigen Values

“DO”

“SO”


Frequency vs. Length

F = const. x (1/L) Guitar Violin Organ

F = const. x (1/L)2

Xylophone

F ~ const. x (1/L)0

Rubber band string


Multi-wire Chambers (1)

When a charged particle passes through, the gas in the multi-wire chamber is ionized.

Electrons drift toward signal wires under electrical field generated by the high voltage wires.

When the electrons arrive the signal wires, electrical pulses are detected.

From arrival time, the track position can be determined.


Multi-wire Chambers (2)

Several planes of multi-wire chambers can be used to determine the track direction.


Straw Tube Chambers

The wire can be stretched in a plastic tube with metalized walls.


Wire Tension Measurement

Wires must be stretched to certain tension to hold their positions. To measure the wire tension, a pulse of current is sent through the wire in a magnetic field. The resonant frequency is recorded to calculate the wire tension.

LmT

Lf

/21

Reflection of Waves


Reflection


Waves reflect at the boundary of two media.

Retro-reflection (1) Animal Eyes


Retro-reflection (2) Mirror Corner


Show the retro-reflectivity of the mirror corner. (using <10 lines)

Retro-reflection (3) Glass Ball


a

b

Glass Balls with Different n


When the index of refraction is ~2, most incident light will reflect back.

Glass Ball Submerged in Water


When the glass ball is submerged in water, relative index of refraction becomes ~ 2/1.33 = 1.5

Most incident light will reflect away. The highway lane paint is difficult to see in rainy nights.

Impedance of Co-axial Cables


Impedance Mismatch & Optical Reflection


The reflection seen above is due to difference of the impedances (not index of refraction!) of media.

Acoustic Impedance Mismatch for Muffler


ImpedanceMismatch

ImpedanceMismatchImpedanceMismatch

ImpedanceMismatch


Sound Wave Reflection at the Tube End

Large fractions of sound waves reflect back and forth in a tube. Different tube lengths cause different resonant frequencies. Small amount of sound waves come out from the tube end or the bell of the

brass instrument. Sound waves reflect at not only closed, but also open ends of tubes.


Signal Reflection in an Open Cable

Cables are usually terminated at the end to eliminate signal reflection. An open cable causes a reflected waveform with same polarity as the transition signal.


An Application: CAKE Clocking

When a signal is sent through a cable, the cable lengths can be different and may change with temperature.

When the pulse is allowed to reflect back, a cake shaped signal is seen at the transmitting end. The width of the cake base can be used to monitor cable lengths.

V/4

R

TDC

w V/4

R

TDC

dA

dB

wdA

dB

w+2dA

w+2dB

w

1

23

1+3

1

2

3

1+3

1 2

3

1 2

3


Oscilloscope View of the CAKE

Two cables with different lengths are used.

CH1 & 3: Transmitting ends.

CH2 & 4: Receiving ends.

Cake shaped pulses are seen at the transmitting ends.


Why a medium has two independent wave properties? A medium has two independent wave

properties: Speed of wave, or index of refraction Impedance

An oscillation is a process of energy exchange between two energy formats: Kinetic energy and potential energy Electrical energy and magnetic energy

The responses of a media to the two energy formats produce two independent wave properties.

Z

v 1

Cherenkov Radiation



Shock Wave of Supersonic Objects

When an object is faster than the speed of sound in air, a shock wave is generated. Bursting balloon: sonic boom. Sneezing: 31 m/s. Initial speed could be higher.


Visible Shock Waves

Supersonic objects cause shock waves. Shock waves cause the water vapor to condense into small ice crystals.


Wake Waves of High Speed Boats

When the speed of a boat is faster than the speed of water wave, a strong wake wave is generated.


Cherenkov Radiation Generated by Fast Charge Particle

When a charged particle moves faster than speed of light in a medium, Cherenkov light is generated.

Faster than speed of light? It is OK in a medium: Speed of light in water: (1/n)*c = (1/1.33)*c

= 0.75 c. Electron at 10 MeV: 0.998 c. Proton at 5 GeV: 0.98 c.


Cherenkov Counter Using Gas

When a particle with speed higher than (1/n)*c passes through the gas, Cherenkov light is generated. Curved mirror focus the light to the photo-multiplier tube (PMT) array. Particle species can be identified. The index of refraction n is adjusted by changing the pressure of gas.

pion

proton

PMTArray


Observation of Cherenkov Light in Atmosphere

Cherenkov light can be generated in atmosphere when cosmic ray particles pass through.


Cherenkov Light in Liquid

Super-Kamiokande water Cherenkov detector


Cherenkov Light in Solid

The detector is used to detect high energy protons for LHC experiments at CERN.

Cherenkov light is generated in fused quartz. Generated light is under total reflection inside the L-shaped bar. (Therefore

the index of fraction of the medium must be > 1.414. ) The light reach the silicon photo multiplier (SiPM) and a electrical pulse is

generated.

SiPM

Multiple Waves in Media



Waves in Media

Two lights (ordinary and extraordinary) in a crystal have different speed and polarizations. Two acoustic waves can be generated in an isotropic solid. Three acoustic waves can be generated in a crystal.

EM WavesOptics

Mechanical WavesAcoustics

Fluid(Gas, Liquid)

1 transverse wave 1 compression wave

Isotropic Solid(Glass, Fused Quartz)

1 transverse wave 2 waves (P and S)

Anisotropic Solid(Crystal)

2 waves (o and e) 3 waves (P, S and S’)


Lights in a Calcite Crystal

Lights with different polarizations have different speed in a Calcite crystal. The phenomenon is called birefringence (double refraction).


Earthquake

The P wave generated by an earthquake arrives earlier than S wave in a seismogram. The distance of the earthquake focus can be estimated from the arrival time difference of the P and

S waves.

Color on Plastic CD Box


sky

It is not due to interference on thin film.

Birefringence (Double Refraction) Due to Internal Stress (Photoelasticity)


The Residual Stress in CD Box


The Residual Stress in Plastic Film


The Sky as a Polarizer


Polarization of Reflection


Brewster Angle

tan(B ) n2

n1

Colors Due to Multiple Effects


sky

Polarized lights are generated in the sky due to scattering. Residual stress in plastic causes double refraction. Double refraction causes polarization plane to rotate and the amount of

rotation is a function of the wavelength. Reflectivity of the plastic surface depends on the direction of the

polarization.

Complexity (or Fun) of Wave Physics



Complexity of Wave Physics

Solid media cause more waves interacting each other. Speeds of waves may depend on the wavelength, i.e., dispersive. Large amplitudes cause the wave equations become non-linear or even chaotic.

Linear range Non-linear range Chaos

Non-dispersive

Dispersive Non-dispersive

Dispersive

Fluid

Isotropic Solid

Anisotropic Solid

College Optics

Earthquake

Tsunami


Nonlinear Optics

There are many amazing effects in nonlinear domain. Frequency of waves can be doubled in nonlinear crystals. When a 1064 nm (infrared) laser is sent through a nonlinear optical crystal

(KDP), a 532 nm light (green) can be generated.


Geological Strata

The earthquake waves travel in layered solid media. The media are usually simplified as isotropic.


Anisotropic Geological Strata?

In reality, rocks can be anisotropic. How rocks become anisotropic is not well understood.


Tsunami

An earthquake sends waves from layers solid to water in deep ocean to start a tsunami. Near the sea shore, the tsunami becomes a shallow water wave which is both dispersive and

nonlinear (or chaotic).

Finale: Why Sine Function is Special



Demo: Reproducing Voice with a Piano

All students come to stage. Howl a vowel into the piano.

Fourier Analysis


x(t) a0 a1 sin(t 1) a2 sin(2t 2) a3 sin(3t 3) ...

Periodic oscillations are decomposed into different frequency components.

Corresponding piano strings resonate.

External oscillation stops, but vibration of piano strings continues.

Human voice is thus synthesized.


Fourier Series

Any periodic function can be expanded into a Fourier series. Mathematically, a periodic function can also be expanded into

other series. Why do we choose the Fourier series?



Taylor Expansion

Using Taylor expansion, a function can be decomposed into linear term and non-linear terms.

Is this decomposition artificial?

f kx bx 2 cx 3 dx 4 ...


Coexistence of Fourier series and the Taylor expansion

The Fourier series is not merely a mathematic expression. There exist physical systems oscillating this way.


f kx md2xdt 2 kx 0 x(t) A1 cos(t) B1 sin(t)

f kx bx 2 cx 3 dx 4 ... The recovery force of real system may not be linear. But it can be arbitrarily close to linear when the amplitude is

arbitrarily small. Linear recovery force causes simple harmonic oscillation:

The End

Thanks

Wave Phenomena

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