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Polarization
blocks TRANVERSE waves of a certain axis of oscillation. Two polarizers in 90 degree = no light. Any angle between will have less intensity/energy going through
Phase difference
Constructive = 0 or 360 degrees, whole # of wavelengths.
Destructive = 180 or any multiple. .5, 1.5, 2.5 wavelengths
Standing waves
When waves with the same amplitude and frequency but opposite propagation. interfere with each other creating the appearance of a wave that isn’t moving set antinodes and nodes.
v=f*lambda, and its amplicatiosn
v depends on the medium, not the wave
f is a property of the wave.
Lambda depends on speed (and thus medium too)
Two types of waves
electromagnetic+tranverse, longitudinal+mechanical (needs medium, like sound).
Waves transfer…
Energy and momentum but not mass.
Pulse vs wave
Pulse is a single oscillation. Wave has to be PERIODIC, repeated pulses.
Longitundal waves
require medium, compressions and rarefractions, movement is parallel to propagation.
v = sqrt(F_T/(m/L))
velocity depends on the force on the medium/string (tension) and the mass density (mass divided by length). Tighter, thinner string has most speed.
Temperature
Sound travels fast when warmer bc it is mechanical and particles are moving faster with more energy/collisions
what is always true of two waves in the same medium?
They are traveling at the same speed.
Graphing a longitudinal wave
time vs pressure, amplitude is loudness. Use sin, -sin, cos, -cos.
Graphing E&M graph
time or position vs electric field or magnetic field strength. Formula is Atrig(2πx/T) substitute x and T as necessary
Types of reflection
Soft reflection, to lower index, no phase change
Hard reflection: from lower to higher index, phase change
Intensity of light can be measured by
Power/Area. Amplitude is proportional to Intensity but no the same. Intensity decreases as you move away from source because more area.
What can you find from an A vs x graph?
wavelength, amplitude. NOT period/frequency bc not in terms of time.
What happens as a wave reaches a boundary?
Reflection, transmission, and absorption. Refraction
How does a particle behave with higher wavelengths
Higher wavelength means lower f (if light), meaning less particle-like and more wave-like, lower energy and momentum. Less diffraction
Experimental design for wave tension/velocity
pulse generator, taut rope, atwood and block to vary F_T. or if its wave, measure the # of sec/# of cycles and do multiple trials.
Harmonic/Sound Exp. Design
Ruben’s tube (gas holes). Tone generator, meter stick, frequency detector (to verify), thermometer. Graph λ = v*T
Dopppler Effect
Closer waves bunch up, so frequency goes up when wavelength goes down, blue shift. Red shift is farther away. Based on relative motion. Nonconstant change in frequency if there’s acceleration. Rapid change in “percieved velocity” as object passes you. Rest frequency
Beats
superposition/interference of waves that are slightly out of phase. The more offset the waves, the quicker and louder the beat/standing wave. Note: only made from wave not pulses
Harmonics
Sound, longitudinal vibrations of air molecules
Differ based on if the ends are fixed or closed.
Both ends fixed/open: λ = 2/(harmonic #*L), or f = (harmonic #)f
One end open: λ = 4/(odd # * L)
Single Slit Diffraction
Fraunhofer diffraction: far enoguh away si that lines from the source can be considered parallel (theta is same)
Wave spreads out because of interference of individual particles. Pattern of constructive/destructive based on phase differences of particles.
y_min (distance from center to first node) = m*λ*D/a
where m is order (which node), D is distance from source to screen, a is width of slit
the shorter part of the slit is the one that spreads out.
Single center dot is width of TWO maxima
What can be said in diffraction if the angle is small?
sintheta = tantheta = theta. So therefore,
x= mλL/d
What affects diffraction
More diffraction with larger λ, smaller opening
Double Slit Diffraction
Typically one brigh spot with gradient on the sides. Rainbowing caused by different in wavelengths.
Further sits = less distance between maxima. Closer λ to object (within a factor of ten, more diffraction)
y_max = mλD/d, where d is distance between slits, D is screen to slits, y is distance between antinodes. Single center dot is width of ONE maxima, not two.
What is ∆D
∆D is the path difference between the particles from each slit. If it is an integer multiple of λ, or where m is an integer 0,±1,±2, then constructive. If .5s then destructive.
Values of m
remember that m measures ANTINODES in double slit, but NODES in single slit. To find the other, you need to take .5’s of m
Experimental Design for Diffraction
Diffraction grating, shine lasers, calculate distance, use distance to find angle, then you know the m to find λ
Resonance
When an external force or vibration matches an objects’ resonant frequency, defined as the frequency that generates the maximum amplitude response in the system
Thin Flim Interference
Things like water drops have reflection at both their inner and outer surfaces that interfere, causing some λs that are brighter/dimmer. Be careful with phase changes at each interface. Film is a THIN layer that is close in thickness to λ. The interference depends on n, λ, and thickness.
Film inteference with 0 or 2 phase changes
λ_film = 4T/(even #) if constructive, odd # if destructive
T is thickness
Film Interference for 1 phase change
λ_film = 4T/(odd #) if constructive, even # if destructive
T is thickness
