4&9 Waves Flashcards
displacement, x [m]
distance in a direction; from equilibrium position
amplitude, Xo [m]
max. displacement from equilibrium position
frequency, f [Hz]
number of oscillations per unit time
period, T [s]
time taken for one complete oscillation
phase difference
difference in the position within a cycle
monochromatic
single color/wavelength
Simple Harmonic Motion (SHM)
acceleration proportional to displacement; directed towards equilibrium position
damping
friction takes away energy from an oscillating system
Describe the energy changes taking place during one cycle of an oscillation
- At max displacement, all Ep
- When released, Ep → Ek
- At equilibrium position, all Ek
- This process is reversed…
resonance
a vibrating system causes another system around it to vibrate with greater amplitude at a specified frequency
wavefront
line joining (neighboring) points IN PHASE; perpendicular to rays
ray
direction in which wave/energy is traveling
transverse vs longitudinal wave
T: oscillation of the particles is PERPENDICULAR to direction of wave travel
L: oscillation of the particles is PARALLEL to direction of wave travel
wavelength, [m]
distance between:
* adjacent troughs/crests (T)
* adjacent compressions/rarefaction (L)
examples of transverse and longitudinal waves
transverse: electromagnetic waves, slinky
longitudinal: sound, slinky
wave speed
v = f x λ = λ/T
energy propagated along a wave per second
wave intensity
I = P/A
power that travels through a given area as the wave travels through
refractive index (n)
n = c/v = light speed in vacuum / light speed in medium = sin(θi) / sin(θr)
the refractive index of air is
1
dispersion
white light separates into its component colors; because different frequencies have different refractive index
diffraction
spreading of waves as they pass through/around an obstacle
reflection
when wave incidents on and bounces off an interface; angle of incidence = angle of reflection
diffraction is most significant when
the size of the gap is similar to the wavelength [pic]
refraction
when wave travels from one medium to another: ∆density → ∆ speed → ∆ direction
Principle of Superposition
when two waves meet → resultant displacement = vector sum of the individual displacements
interference
when waves from two coherent sources SUPERPOSE (resultant displacement = vector sum of the individual displacements)
* path difference = nλ = constructive
* path difference = (n+0.5) λ = destructive
Rayleigh Criterion
will be able to resolve (distinguish two sources as being separate) when the max of one diffraction pattern is coincident with the 1st min of the other
Distinguishing between standing and traveling waves
traveling: TRANSFER ENERGY; can have ANY FREQUENCY
standing: zero net energy transfer; have discrete frequency
Describe the nature and formation of standing waves
wave travel down the tube→ gets REFLECTED→ INTERFERENCE (superposition) between incident and reflected wave
Explain how energy is transmitted in sound wave
Particles vibrate in the same direction as energy transfer → causes nearby particles to vibrate
Describe the motion of a particle at equilibrium during the passage of the next complete transverse wave
Oscillate perpendicular to energy transfer ep→Max→ep→Min→ep
Explain the effect of a polarizer on light intensity
oscillation of light waves from all directions to ONE PLANE only → intensity halves!!
Distinguish between polarized and unpolarized light
Unpolarized: electric field vector vibrate in ALL PLANES
Polarized: electric field vector vibrate in ONE PLANE only
Explain how polarizing sun glasses reduce glare from a reflecting surface
Light is horizontally polarized by reflection → sunglasses have a perpendicular transmission axis to the plane of reflected light → reduce intensity
construtive interference
waves are IN-PHASE when they meet → produce a greater resultant displacement
Two overlapping beams of flashlight fall on a screen but no interference pattern is observed - explain why
There IS interference! But since the phase between the two sources is rapidly changing, the interference pattern is also CHANGING TOO RAPIDLY to be observed.
optically active substance
rotates the plane of polarization of incident polarized light
Explain why diamonds sparkle
due to TIR!! diamonds have very small critical angle → easier to sparkle
Critical Angle
angle beyond which TIR occurs
n = 1/sinθc
What is the condition for Total Internal Reflection (TIR)?
incident angle ＞ critical angle
Imagine you’re sitting at the bottom of a swimming pool - explain what you see when you look up
can only see limited sight of above water as the rest will be reflection of the bottom due to TIR
explain the single slit diffraction pattern
- waves diffract because even the narrowest slit is much wider than the wavelength of light
- waves diffracting away from the slit can be considered as a series of wavelets originating from imagined separate sources one wavelength apart from each other.
- these wavelets superpose with each other to produce an interference pattern
suggest 3 ways to increase the fringe width of a single slit diffraction?
fringe width = θ = λ/b
- increase wavelength λ (eg. use red light)
- decrease slit width b
- moving the screen further away, so that waves travel further distance and spread out more
describe and explain the single-slit diffraction pattern of a white (not monochromic) source
white central max+colorful other max (violet = shortest λ = least diffracted = nearest to central max, red = longest λ = most diffracted = furthest from central max)
Explain how optic fiber works
θi ＞θcso light travels down the cable by bouncing off the walls due to TIR
range of the visible spectrum’s wavelength
380-700 nm
In a double slit experiment, there is a missing fringe on the screen - explain why
double slit interference is modulated by the single slit diffraction pattern; double’s max + single’s min = 0 intensity
describe what happens to the fringe pattern when a double slit is replaced by a diffraction grating (very large number of narrower slits)
- more light get through → brighter fringes
- more path with destructive interference → shaper fringe
- smaller b → bigger θ → fringes further apart
Doppler effect
change in observed frequency of a wave; as a result of RELATIVE motion between source and observer
RED shift happens when stars
move AWAY from us → longer wavelength→ shifts to red spectrum
what happens to the single slit diffraction pattern when a BLUE laser is replaced by a RED laser?
θ = λ/b
λ increase → bigger angle of diffraction → wider fringes
what happens to the single slit diffraction pattern when the slit if made narrower?
- intensity decrease
- fringe spacing increase (θ = λ/b)
nλ = d sinθwhat do the letters reprsent and when is this formula used?
used for diffraction gratings
* n = order of maxima
* d = distance between slits
* θ = angular separation between maxima
θ = λ/b = X/Dwhat do the letters reprent and when is this formula used?
used for single slit
* θ = angle of diffraction
* λ = wavelength of source
* b = slit width
* X = separaction of sources
* D = distance btwn source and observer
sd = λD what do the letters reprent and when is this formula used?
used for double slit
* s = distance between fringes
* d = distance between slits
* λ = wavelength of source
* D = distance btwn slit and screen
2dn = (m+0.5)λwhat do the letters reprent and when is this formula used?
thin film interference (constructive, 1 phase change)
* d = thickness of the film
* n = refractive index** of medium
* m = any integer, ‘thinnest film’ when m=0
* λ = wavelength of the light IN AIR
R = λ/∆λ =mNwhat do the letters reprent and when is this formula used?
Rayleigh Criterion
* R = resolving power
* λ = wavelength of incident light (m)
* Δλ = difference in wavelength
* m = order of diffraction*
* N = number of slits on the diffraction grating illuminated by incident light)
Describe, in terms of molecular movements, how sound travels from our throats to somebody’s ear.
the vocal chords in our throat vibrate → disturbs surrounding air → air molecules oscillate as longitudinal waves → collide with our ear drums and make them vibrate at the same frequency
path difference
the difference in distance travelled by two waves from their sources to a given point.
path difference = nλ = constructive
path difference = (n+0.5) λ = destructive
Explain why the pattern seen on a screen when white light passes through double slits is colored
white light contains a continuous range of different wavelengths → travel at different angles after diffraction → constructive interference at different places on the screen
Explain why anti-reflection coatings on lenses need to be λ/4 thick
light reflecting off both surfaces will undergo a phase change of π as the material is less dense than glass → the condition for destructive interference becomes 2d=λ/2
What is ultrasound?
sound with frequency higher than human can hear
What is the assumption behind using ∆f/f ≈ v/c
c»_space; v
A girl looks at a flat vertical glass window with a think transparent coating. Explain why the light reflected to the girl has one wavelength missing.
There is partial reflection at the front surface of the layer AND the glass-layer interface; missing wavelength is where destructive interference between reflected rays occurs
