EK Physics Chapter 5: Sound and Light Waves

2 characteristics of a media that determine velocity of waves thru it:

- media's elasticity (resists change in shape) - media's inertia (resists change in motion) no other characteristics (besides temperature) do - frequency, for ex, does not change velocity through a medium.

3 ways an electron can receive the energy needed to move from ground to excited state:

1. atom w/ e- could be bombarded by high speed particles like other electrons. 2. atom could absorb a photon of light 3. atom could be subject to thermal agitation (electrons in closely packed atoms can transition between energy levels of the same atom or different atoms, which emits incandescent light).

Thus, thin film interference is the result of three factors:

1. phase changes associated with reflections off media that are more dense. 2. path length differences 3. wavelength changes associated with changes in media.

3 keys:

1. to solve for Doppler effect: when wave source + observer move toward each other, frequency increases -add delta f to f_s to get f_o. Vice versa when wave source and observer move away. 2. determine whether a wave is undisturbed, reflected, refracted, diffracted, or dispersed. 3. lenses and mirrors follow the three optics rules: focal point rule, object rule, image rule.

EM wave formed by:

a charge vibrates, accelerating and producing a changing elec field. this movement of charge creates a changing mag field that in turn can induce a changing elec field. as elec and mag fields regenerate each other, a traveling oscillation of an elec and mag field (an EM wave) emanates from the vibrating charge.

intensity level

a measure of loudness - describes how intense a sound seems to be, to the human ear.

diffraction grating:

a series of many small slits that diffracts a light source into its component colors. produces spectra of the component parts of the light source from shorter wavelengths (violet) to longer (red)

pitch

can describe sound waves - how high or low a note sounds, and so is correlated with frequency. high note has a high pitch and a high frequency.

shock waves

conical wave front, produced when velocity of sound source exceeds velocity of the sound wave. like any sound wave, a shock wave consists of oscillations between high and low pressures. when source moves faster than speed of sound, many wave fronts overlap, generating region of very low pressure. air moves in direction of pressure gradient, and rapid movement creates loud sonic boom.

constructive vs destructive

constructive: sum of displacements = greater displacement. destructive is smaller displacement

formula for maxima produced by a diffraction grating is the same as that for the double slit experiment:

d*sin(theta) = m*lambda for m=1,2,3

Understand (don't need to memorize) equations for maxima and minima (bright portions from constructive interference and dark portions from destructive, respectfully): Note: Remember the +1/2 term for maxima because maxima are 'larger' than minima.

maxima: 2L = (m+1/2)*lambda/n2 for m=0,1,2,... minima: 2L = (m)*lambda/n2 for m=0,1,2,... L = thickness of thin layer, n2 = index for thin layer.

Maxima and minima in double slit diffraction:

maxima: when path difference delta = d*sin(theta) = m*lambda for m=1,2,3 minima: path difference delta = d*sin(theta) = (m+1/2)*lambda for m = 1,2,3

resonance in pipes and strings

most common way for resonance to occur on the MCAT. sound waves in pipes/strings. String may have one or both ends fixed; pipe may have one or both ends open. pipes create longitudinal waves; strings make transverse waves.

** a medium's index of refraction:

n, the ratio of speed of light in a vacuum to light's velocity in the particular medium (v): n = c/v Thus, the greater the index of refraction, the more slowly light will move thru that medium.

'c' of a wave:

not necessarily the speed of light, c stands for the velocity of the wave in the given medium.

frequency

number of wavelengths past a point per second. determined by wave source - it does NOT change as medium changes.

mechanical waves

obey the laws of classical mechanics, and require a medium through which to travel. sound/wave on string waves are examples.

amplitude

of a wave; represents the max displacement - if measured by a sine graph it is the distance from x axis to crest of wave. can change thru mediums.

* thin film interference

particular type of interference that enhances or diminishes certain wavelengths of light: a thin layer of 1 substance is placed between two layers of another substance with a different index of refraction.. At each interface, light can reflect or refract. refract: changes wavelength but not phase. reflect off a denser medium: changes phase, not wavelength. reflect off less dense medium: changes neither wavelength or phase.

Mach number

ratio of the velocity of the source to velocity of the wave: v_s / v

attenuation/damping

real waves undergo damping - the decrease in the intensity of a wave propagating through a medium. reflection is one cause, absorption is another example.

Light thus bends in 3 ways:

reflection, refraction, diffraction. Longer wavelengths diffract more, but refract less than shorter wavelengths.

oscillations

regular variation. in sound waves = variations between high and low pressure.

shorter wavelengths = longer wavelengths =

shorter wavelengths (high frequency) = violet (then UV) longer: red (then infrared)

'colors' that are observed:

show the wavelengths of light that an object does NOT absorb - the reflected wavelengths. black - all wavelengths of light are absorbed. white - no wavelengths of light are absorbed.

** Snell's law:

shows the extent to which a change in speed will bend a light ray: n1sin(theta1) = n2sin(theta2) theta1 is angle of incidence and theta2 is angle of refraction. Both, again, are measured from normal to the surface.

standing wave

situation where two sine waves with same wavelength collide, and nodes/antinodes created nodes = max destructive interference, so the point does not move. antinodes = maximum constructive interference, with high amplitude.

wave equation, speed of light + wavelength + frequency:

v = f*lambda So, f = c/lambda.

In general:

v(sound wave in solid) > v(sound in liquid) > v(sound in gas)

EM spectrum

visible light, in increasing freq and decreasing wavelength, goes: ROY G BiV (red orange yellow green blue,indigo, violet). This continues to UV, x ray, gamma ray. On the lower frequency side, it goes infrared, microwave, radio wave, long waves (which have the longest wavelengths).

MCAT: know indexes of refraction (n=c/v) for water, glass, air:

water: 1.3 glass: 1.5 air: 1.0

reflection and refraction

when a wave reaches interface between two media, it can be reflected back into media it came from or bend thru refraction into new media.

polarization of light

when light's elec and mag fields are oriented in a particular, rather than a random, way. if horizontally polarized: elec field oscillates parallel to the x axis. if vertical, elec field oscillates parallel to y axis. in all cases, mag fields oscillate in planes perpendicular to the planes in which elec fields oscillate.

interference

when two or more transverse waves superimpose, and their displacements add at each point to make a new wave

chromatic dispersion

when white light - made up of all light frequencies in the visible spectrum - is split by a prism and distinctive wavelengths move at slightly different speeds -> rainbow spectra of color.

x ray diffraction

x rays have wavelengths of about 1 angstrom, about diameter of an atom. Since diffract works best when opening is size of a wavelength or smaller, a diffraction grating can't be mechanically created, but a crystal has the evening spacing between atoms to work as a natural x ray diffraction grating. x rays projected at crystal -> scatter -> make regular interference patterns unique to structure of the crystal.

circularly polarized light

light that consists of elec fields of constant magnitude that change direction in rotary manner (fields can rotate in either CW or CCW direction).

absorption

likelihood that any wave will be absorbed depends on medium + frequency of the wave

sound

transfer of energy thru oscillations between high and low pressure.

x ray diffraction maxima from Bragg's Law: (just be prepared for possible question, don't memorize. will be given if we need it).

2sin(theta) = m*lambda, for m =1,2,3 So it can be used to analyze crystalline structure.

standing waves cause a string to resonate:

= vibrate at a string's natural frequency or resonant frequency

beta; the artificial log scale for intensity level measured in decibels dB:

B = 10 log(I/I_o)

Depending on changes in wavelength, phase and path length, constructive or destructive interference can occur.

Basically, angles of incident light will result in parallel angles of reflected light, but some of the refracted light will also come back into the original media if it is reflected off the back wall of the middle media and refracted through the front wall of the middle media. This twice-refracted light ray will come out parallel to the originally reflected portion of the incident light ray, and depending on wavelength, film thickness and phase, will either interfere constructively or destructively. (p. 147)

energy of photon

E=hf When f falls in visible spectrum, human eye perceives a color.

phase

MCAT: enough to think of the phase as horizontal shift of a wave on xy plane - each wavelength is 360 degrees, so half of a wavelength of phase shift is 180 degrees.

Calculating relative velocity:

Think about the net velocity between 2 objects (observer and source) - its intuitive, if they are traveling the same direction, subtract their velocities because in relation to each other, they're not going as fast. if moving toward or away from each other, they are going relatively faster than their individual velocities, so add the relative velocities.

relationships between n, v, lambda:

Two key equations; n =c/v and v=f*lambda. Thus an increase in n corresponds to a decrease in v and decrease in lambda. An increase in n (going from lower to high index of refraction, i.e. air to water/glass): decrease in v and decrease in lambda.

When to use +/- signs for v_o and v_s?

When either is moving towards the other, f_o>f_s, so the factor by which f_s is multiplied must be > 1. Thus it must be c+ v_o in numerator and/or c-v_s in denominator. The opposite is true for either observer/source moving away.

example of TIR:

You must have light going from higher to lower n, say from glass to air (1.5 to 1). If light hits interface at critical angle, angle of reflection is back into glass (at same angle to normal as the critical angle) while angle of refraction would be directly along interface, which would be 90 degrees to normal. no refraction should occur in this case.

visible light includes:

all wavelengths from 390-700nm , or 390*10-9m - 700*10-9m

angle of incidence

angle at which a wave strikes an interface. reflects at the angle of reflection

critical angle

angle of incidence at which all light becomes internally reflected; no refraction occurs.

know speed of light in a vacuum for MCAT:

c = speed of lift in vacuo = 3*10^8 m/s.

Young's double slit experiment

light projected onto screen with two small slits. the light waves diffracting through the 2 slits interfere with each other and produce a predictable pattern of alternating maxima and minima. The diffracted waves start out in phase, but travel different path lengths to meet on the detector.

**Doppler effect for all waves can be approximated by: (use this eqn instead of previous for MCAT)

delta f / f_s = v/c and delta lambda / lambda_s = v/c Can then add/subtract the change in frequency/wavelength to the source frequency/wavelength to get the observed f/lambda.

** speed of vehicle calculation via Doppler effect and beat frequency as measure of delta f:

deltaf/f_s = 2v/c OR v=c*delta_f/2f_s

wavelength

distance from any point in wave to the point where the wave begins to repeat itself.

wave velocity

distance wave travels over time, determined by the medium. v = f*lambda (lambda is wavelength, = distance. frequency is the inverse of time)

EM waves

do not require medium; can propagate in vacuo(vacuum). ex: light

light from lower n to higher n:

light ray bends TOWARD normal (speed decreases and its like hitting sand; this curves the light ray toward normal; deeper into the new medium). exception: angle of incidence = 90degrees means that no bending occurs.

**beat formula Important to know/understand/be able to use on MCAT.

f_beat = |f_o - f_s| This provides a measure of the change in frequency. Important to note that you can then calculate the speed of a vehicle approaching you (ex:speeding car approaching police car), but you must take Doppler effect into account twice, as radio waves emit and hit car, then are emitted again from car to hit police scanner.

formula for Doppler effect (will be given on MCAT if needed):

f_o = f_s (c+/-v_o / c+/-v_s) f_o = observed frequency, f_s = source f.

* refraction does not change the phase of the wave at the interface between two media, nor does it change the frequency. it changes wavelength, and thus velocity/

if new medium's n is larger, wavelengths become shorter. if n is lower, then the wavelengths become longer.

incandescent light vs fluorescent light

incandescent - exhibiting a continuous range of wavelengths (often due to thermal agitation). fluorescent - wavelengths in visible light range (often due to absorption of a light photon)

total internal reflection

light coming from medium with higher n, angle of incidence can be large enough that all photons will be reflected at the angle of reflection, and none will refract. this angle = critical angle.

light going from higher n to lower n:

speed increases and the wave fronts spread out, thus the light ray bends AWAY from normal, so more shallow into the medium.

Doppler effect

the change in perceived frequency that occurs when a wave source and its observer move towards or away from each other. moving towards: observed frequency higher than source freq. away: observed f lower than source f.

resonance

the condition where the natural frequency and driving frequency (driving the wave) are equal.

'beat' frequency

the difference between observed and source frequency (proportional to how often the waves interfere constructively vs destructively). can also describe difference in frequency between two sounds.

transverse v longitudinal

the direction the medium is displaced - transverse = opposite propagation, longitudinal is with propagation. sound is longitudinal.

photons

the light emitted from excited electrons (emitted in transition from higher to lower energy levels): pulses of electromagnetic radiation; can be thought of as localized particles of energy.

wave

the propagation of a vibration from one point to another.

dispersion

the separation of light into different frequencies due to their different indices of refraction in a medium. due to index of refraction varying slightly with frequency (and therefore with wavelength).

diffraction

the spreading of light when a wave bends around the edges of an object or opening. Significant when the size of an object or opening is small relative to the wavelength of a wave. the smaller the object/opening and the larger the wavelength, the greater the bending of the wave. Basically: the interference patterns formed when light passes through slits.

light

the transfer of energy through alternating electric and magnetic fields.

open vs closed ends of a pipe

there does not have to be a closed end, but must be at least 1 open end. an open end is a particle displacement antinode(high amplitude of particle displacement) and a pressure node (no pressure differential). closed end has no particle displacement but greatest pressure differential, so pressure antinode and displacement node.

** critical angle derived from Snell's Law:

theta(critical) = sin^-1 (n2/n1)

Young's diffracted waves met constructively/destructively when:

they met constructively when the difference in path length, delta, was a multiple of lambda. destructively when delta was a multiple of lambda/2.

I_o :

threshold intensity of human hearing (lowest intensity audible by the typical human)

period, T

time it takes wave to travel one wavelength's distance. does not change with medium