How Light and Sound Interact With Matter

How light and sound interact with matter Sound (PHY) • Production of sound o Occurs via vibration of a source which produces waves ▪ Waves: propagation of a vibration from one point to another. Often seen as transferring energy from point to point • Mechanical wave: needs a medium through which to propagate (sound) o Longitudinal wave: displaces medium parallel to direction of wave propagation o Transverse wave: displaces medium perpendicular to wave propagation • Electromagnetic wave: doesn’t need a medium to travel through (light), can travel in a vacuum • Relative speed of sound in solids, liquids, and gases o Wave’s velocity is determined by the medium it travels through (for both sound and light waves) ▪ If a wave travels from one medium to another, its velocity changes ▪ Velocity increases proportionally with the temperature of the medium ▪ Frequency is not changed when a wave switches mediums. Wavelength changes. • Frequency is determined by the wave’s source. Wavelength is determined by the medium o Two characteristics of a medium that dictate velocity of waves ▪ 1) Elasticity, or its resistance to change in shape • Increase in elasticity results in an increase in velocity • Increases as intermolecular attractions become stronger ▪ 2) Inertia, or its resistance to change in motion • Increase in inertia results in a decrease in velocity • Decreases as mass and density increase o V = λf ▪ Velocity equals frequency*wavelength • Effectively a measurement of distance over time. Wavelength is distance. Frequency is time. ▪ Period: the time it takes for a wave to travel one wavelength • P = 1/f ▪ Increase in velocity is associated with an increase in wavelength • Intensity of sound, decibel units, log scale o Measure of average rate of energy transfer per unit area, the power of a wave o Depends on density of medium, wave frequency, and wave velocity ▪ Directly proportional to the squares of frequency and amplitude (these two factors have the largest effect on intensity) o Total energy is constant for a propagating wave ▪ As a wave propagates outwards, its SA increases. This causes intensity to decrease (less energy per SA) o Log scale ▪ Decibels: describes how loud a sound seems to be (intensity level) • Has a logarithmic relationship to intensity ▪ Intensity level = 10log (I/Io) • I = final intensity value, Io = initial intensity level • Key takeaway: If the intensity of a sound increases by a FACTOR of 10, the decibels (intensity level) increases by an ADDITION of 10 • Attenuation (Damping) • • • Doppler Effect: moving sound source or observer, reflection of sound from a moving object o Moving sound source ▪ Change in frequency • As source moves TOWARDS an OBSERVER, relative distance between wavefronts decreases, INCREASING THE FREQUENCY • Doppler effect is associated with a change in frequency ▪ Doppler formula • Δf/fs = v/c AND Δλ/λ = v/c o Δf = change to the source frequency, fs = source frequency, v = relative velocity of the source and observer, c = wave velocity • Fo = fs +/- Δf AND λo = λ +/- Δλ o Reflection of sound ▪ Beats • Sound can be emitted from a stationary observer, bounce off a moving object, and get back to that observer with a different frequency ▪ Formulas • Δf/fs = 2v/c o Exactly the same as the other formula except you are multiplying velocity by 2 ▪ This makes sense because sound needs to travel twice over the same distance Pitch o A measure of how “high” or “low” something sounds o Correlates with frequency ▪ High note has high f, low note has low f Resonance in pipes and strings o String: generates transverse waves ▪ Fixed at both ends: ends of strings are nodes o Pipes: generates longitudinal waves ▪ Both ends open • Air particles at open end move with maximum displacement (free to move b/c not confined to the pipe as the ends are open) • Pressure at both ends are relatively equal ▪ One end closed • Air particles are closed end cannot oscillate • Air pressure is greater at closed end (wave bounces off wall, particles at end pressed against closed end of the pipe) ▪ Both ends closed • Air particles at closed ends move with zero displacement and generate max pressure • Air pressure at both ends are relatively equal o Node vs. Antinode ▪ Node: point of maximum destructive interference for a wave collision (two waves converge to a single point) • Nodes are present at the closed end of a pipe and on the ends of a fixed string ▪ Antinode: point of maximum constructive interference for a wave collision (two waves’ peaks are farthest apart) • Antinodes are present at the open end of a pipe o Attenuation ▪ Decrease in amplitude of a wave • • ▪ Can be caused by reflection or spreading of sound waves ▪ Attenuation causes intensity to decrease o Harmonics ▪ L = lambda(n/2) • L = length of string producing sound, n = harmonic of sound produced • Lambda = 2L/n o Shows that wavelength = twice the length of the string over the number harmonic of sound produced ▪ fn = nf1 • Shows that harmonic frequency = n times the fundamental frequency. 1 st harmonic is 3 times the fundamental frequency, etc. ▪ Beat frequency: frequency produced when two tones with different frequencies are emitted at the same time • Beat freq. = | f2 – f1 | n Ultrasound Shock waves o Conical wave front produced when velocity of the sound source exceeds the velocity of the sound o Mach number ▪ Ratio of the velocity of the source over the velocity of the wave ▪ Mach number = vs/v Light, Electromagnetic Radiation (PHY) • Concept of Interference: Young Double-Slit Experiment o Concept ▪ Light waves that are out of phase collide, undergo destructive interference o Young’s Double-slit Experiment ▪ Monochromatic light is projected onto two small slits, split into two beams which create light/dark patterns ▪ Path length difference: difference in lengths that light from two slits travel to reach a certain point ▪ Constructive Interference occurs when path length difference between is a multiple of lambda ▪ Destructive Interference occurs when path length is a multiple of lambda/2 ▪ Formulas for maxima and minima • Max: dsinθ = mλ • Min: dsinθ = (m+1/2)λ o Θ = angle between the 0th order maximum and the mth order maximum; m = order of the maximum (1, 2, 3, ….); d = distance between the slits • Thin films, diffraction grating, single-slit diffraction o Thin film interference ▪ Main idea: light shown at a thin film can undergo constructive or destructive interference • Sub idea: light undergoes a phase change of ½ when it reflects off a material with a greater index of refraction ▪ Destructive interference • Thin film thickness is a multiple of ½ the wavelength of light, reflected and refracted light rays are in phase o Note: When light reflects off a thin film, it undergoes a phase change of ½ ▪ Constructive interference • Thin film thickness is a multiple of ½ the wavelength of light, reflected and refracted rays are out of phase Note: if the material behind the thin film has a higher index of refraction, then the above formulas are switched around (b/c it undergoes another phase change of 1/2) • Destructive interference is now caused by a film with a thickness of a multiple of ¼ the wavelength • Constructive interference is now caused by a film with a thickness of ½ the wavelength o Diffraction grating ▪ Light is passed through many slits spaced very closely together ▪ More slits = narrower and more defined maxima, wider dark regions between maxima ▪ Uses same formulas as double-slit diffraction Other diffraction phenomena, X-ray diffraction o X-ray diffraction ▪ X-rays diffracted by passing them through crystals • X-rays have VERY small wavelengths. Crystals’ atoms have spacing around the same wavelength as x-rays, allowing for diffraction • Rays reflect off of distinct surfaces within the crystal (reflecting planes) ▪ Formulas • 2dsinθ = mλ o d = distance between reflecting planes; θ = angle between the reflective plane and the ray ▪ • • • • o Polarization of light: linear and circular o Linear ▪ Polarization in x or y axis ▪ Light that’s vertically polarized passing through a horizontal polarizer will be made unpolarized o Circular ▪ Electric fields of constant magnitude changing direction in a rotary manner produces circularly polarized light Properties of electromagnetic radiation o Velocity equals constant c, in vacuo ▪ Can proceed in vacuum (doesn’t need a medium to propagate through) o Electromagnetic radiation consists of perpendicularly oscillating electric and magnetic fields; direction of propagation is perpendicular to both Classification of electromagnetic spectrum, photon energy E = hf o Order of electromagnetic spectrum (highest to lowest wavelength) ▪ Radio waves → infrared → visible light → ultraviolet → x-rays → gamma rays o Light is produced when an electron transitions from higher (excited) to lower (ground) energy states ▪ 3 ways an electron can move to higher (excited) energy states • 1) An atom is bombarded by high speed particles (i.e. electrons) • 2) An atom absorbs a photon of light o When the excited electron loses E, it emits fluorescent light • 3) An atom is subjected to high temperatures • o When the excited electrons lose E, they emit incandescent light o Deriving frequency from wavelength ▪ Freq. = c/λ Visual spectrum, color o 3.90*10^-9 to 9*10^-9 nm wavelength spectrum o Wavelengths of color (highest to lowest) ▪ Red → yellow → green → blue Molecular Structure and Absorption Spectra (OC) • Infrared region o Intramolecular vibrations and rotations ▪ Infrared radiation used to create vibrations and rotations in intermolecular bonds ▪ Intermolecular bonds vibrate at different frequencies. When frequency of infrared radiation = resonance frequency of a bond, that bond absorbs IR energy. • IR measures frequency of absorption o Recognizing common characteristic group absorptions, fingerprint region ▪ 1600 to 3500 cm^-1, most predictable section of IR spectrum ▪ Bond absorptions • C=O: 1710, single peak • O-H (carboxylic acid): 2500-3000, broad peak, overlaps with C-H • O-H (alcohol): 3300, single peak • C-H (saturated): 2800-3000, multiple peaks • C-H (aldehyde): 2700, single peak • C-N: 2200, single peak • N-H (amine): 3300, small nipple-shaped peak • N-H (amide): 3300, large double pick ▪ Fingerprint region • 600 to 1400cm^-1 region, complex vibrations that distinguish similar compounds from one another • Visible region (GC) o Absorption in visible region gives complementary color (e.g. carotene) ▪ Compound with 8 or more double bonds have absorbance in visible region ▪ Ex. Beta-carotene • Precursor of vitamin A found in carrots, 11 conjugated double bonds, absorbs blue-green light o Reflects complementary color red-orange, giving carrots this color o Effect of structural changes on absorption (e.g. indicators) • Ultraviolet region o π-Electron and non-bonding electron transitions ▪ UV light bumps pi electrons from bonding to non-bonding orbitals (from HOMO to LUMO) ▪ In conjugated systems, HOMO and LUMO are much closer ▪ Pi electron movement from HOMO to LUMO changes absorbance of compound o Compound systems ▪ Conjugated systems absorb more UV rays than nonconjugated systems ▪ A = εcl • A = absorbance, ε = molar absorptivity, c = product of concentration of sample, l = path length of light through cell • Absorbance dependent on inherent absorptivity of compound, concentration of compound, and distance it has to travel through compound • • NMR spectroscopy o Concerned with hydrogen atoms, other odd-number elements o Protons in a magnetic field; Equivalent protons ▪ Spin states • Protons in nuclei can have their rotations aligned with (alpha) or against (beta) an external magnetic field o Beta nuclei are in higher energy state • Nuclei can be induced to go from low-energy alpha to high-E beta by photon collision • When they go back to alpha, they release energy which is detected by NMR ▪ NMR spectrum • Graph of magnetic field strengths absorbed by hydrogen, carbon, other oddnumber atomic number atoms at a specific frequency o Magnetic field strength varies but frequency is held constant • Greater area of a peak = greater number of H’s there ▪ Chemically equivalent protons/hydrogens • Groups of hydrogens denoted by the same peak on NMR • These are hydrogens whose position on a compound is indistinguishable via NMR o Electron-shielding ▪ Position of peaks dictated by electron shielding • Electron withdrawing groups lower shielding → decrease magnetic field strength required for resonance → peaks are more downfield • Opposite true for electron donating groups o Integral trace ▪ Line drawn above peaks that rises each time it goes over a peak ▪ Rise is proportional to number of chemically equivalent hydrogens in the peak beneath it o Spin-spin splitting ▪ Splitting of peaks caused by neighboring hydrogens • Neighboring hydrogen: hydrogen connected to an atom adjacent to the atom the other hydrogen is connected to ▪ Number of peaks = n + 1 • N = number of neighboring hydrogens ▪ Carbon-13 NMR does NOT have splitting Mass Spectrometry o Uses electron bombardment instead of electromagnetic radiation Geometrical Optics (PHY) • Reflection from plane surface: angle of incidence equals angle of reflection o Angles (measured from a line NORMAL to the surface) ▪ Angle of incidence: see below ▪ Angle of reflection: angle at which light reflects off a surface • Refraction, refractive index n; Snell’s law: n1sinθ1 = n2sinθ2 o Angles (measured from a line NORMAL to the surface) ▪ Angle of incidence: angle at which light strikes a surface ▪ Angle of refraction: angle at which light is refracted on other side of surface o Refraction’s effects on light’s properties ▪ Frequency: not changed ▪ Wavelength: changes • From lower to higher index of refraction, wavelength decreases • From higher to lower index of refraction, wavelength increases ▪ • • • • Velocity: changes • From lower to higher index of refraction, velocity decreases and wave fronts cluster closer together • From lower to higher index of refraction, velocity increases and wave fronts get more spread out o Snell’s Law ▪ Measures extend to which light is bent when transferring between mediums Dispersion, change of index of refraction with wavelength Conditions for total internal reflection o Critical angle = sin-1(n2/n1) ▪ At the critical angle, no light is refracted Spherical mirrors o Center of curvature (R) ▪ Radius of curvature of mirror, all points on curved mirror are equidistant from this o Focal length ▪ F = R/2 ▪ Point where light rays actually converge/appear to converge o Converging and diverging mirrors ▪ Converging • Light rays converge in front of mirror • Created by concave mirrors ▪ Diverging • Light rays coverge behind mirror • Created by convex mirrors o Real and virtual images ▪ Virtual: upright image on the opposite side of the observer, same side as the object (negative sign) • Diverging mirrors and lenses always form virtual images ▪ Real: inverted images on the same side as the observer, opposite side of the object (positive sign) • Converging lenses and mirrors can form BOTH virtual and real images o Mirrors: beyond focal point = real; Within focal point = virtual o Lenses: beyond focal point = virtual; Within focal point = real Thin lenses o Converging and diverging lenses ▪ Converging • Light rays converge opposite of the object side of lens • Created by convex lenses ▪ Diverging • Light rays converge on object side of lens • Created by concave lenses o Use of formula 1/p + 1/q = 1/f, with sign conventions (Thin Lens Equation) ▪ Used to calculate object distance (p) and image distance (q) for mirrors or lenses ▪ Sign conventions • p: positive when objects are "where they belong" (on observer side for mirror, object side for lens) • q: positive when image is real (same side as observer), negative when image is virtual (opposite side as observer) • f: positive for a converging lens or mirror, negative for a diverging lens or mirror o Lens strength, dopters ▪ Magnification • • • • • o h = height of image/object o d = distance of image/object from the mirror/lens Diverging vs. converging o Diverging mirrors/lenses always form smaller images o Converging mirrors/lenses form larger images UNLESS the object is outside their radii of curvature Combination of lenses o How to deal with these problems ▪ One lens at a time, consider the image of the first mirror/lens as the object of the second o Magnification ▪ M = M1M2 ▪ Magnification of a two-lens system = products of magnification of lenses o Power ▪ P = P1 + P2 ▪ Power = sum of the powers of the two lenses o Practical applications ▪ Microscopes and telescopes • 2 lenses: objective and eyepiece • Light first hits the objective, which creates a real, inverted image • Image created by the objective acts as the object for the eyepiece, which flips it to be a virtual upright image o Image created by telescope/microscope appears inverted ▪ Human eye • Cornea bends light a LOT, lens bends light a little for fine control • Focusing on… o Near objects: ciliary muscles contract, making lens bulge and making focal point closer to lens o Far objects: ciliary muscles relax, making lens thin and making focal point farther away from lens • Myopia and hyperopia o Myopia (nearsightedness): lens bends light too much, corrected with diverging lens o Hyperopia (farsightedness): lens doesn’t bend light enough, corrected with converging lenses Lens aberration o Only parabolic lenses have a single focal point ▪ Spherical lenses may produce distorted images o Chromatic Aberrations ▪ Higher frequency light focuses closer to the lens than low-frequency light • Only occurs if light of different frequencies pass through a lens simultaneously o Spherical aberrations ▪ Only parabolic lenses have a single focal point ▪ Rays further from the center of the lens arrive at a different focal point than those closer to the center Optical Instruments, including the human eye