IB Physics Topic 4 Oscillations and Waves and Topic 11 Wave Phenomena

Outline qualitatively the action of liquid-crystal displays (LCDs).

•The particles in LCDs can change positions and therefore the plane of polarisation can rotate •liquid crystal is put between two glass electrodes and is birefringent •with no liquid crystal between electrodes, second polariser would absorb all light passed through first, screen would appear black •liquid crystals has a twisted structure, and in absence of potential difference, causes plane of polarisation to rotate 90° •no p.d, LCD appears light •p.d. liquid crystals cause molecules to align with electric field, appear darker

Describe polariods.

•The polarizing materials are called polaroids. •Arranging two polaroids at right angles will result in a block of nearly all light, since the nature of the materials blocks all of the horizontal waves and then all of the vertical waves (or wave components) •after light passes through a polaroid, it will have intensity=½I₀

Sketch the variation with angle of diffraction of the relative intensity of light diffracted at a single slit.

•When light passes through a narrow slit, it spreads out due to diffraction. The spreading out is not uniform but forms a pattern. •Central maximum intensity, other maxima occur roughly halfway between the minima •angle of first minimum is given by sinθ=λ/b but for small angles this can simplified to θ=λ/b •as the angle increases the intensity of the maxima decreases

Calculate the intensity of a transmitted beam of polarized light using Malus' law.

•When plane-polarised light is incident on an analyser, the intensity of light is measured in a single plane of vibration •I₀ is the intensity of the polarized light (½ that of the unpolarized light) and I is the intensity of out transmitted polarized light. •I=I₀cos²θ

State that all electromagnetic waves travel with the same speed in free space, and recall the orders of magnitude of the wavelengths of the principal radiations in the electromagnetic spectrum.

•charges that are accelerating generate electromagnetic fields •if an electric charge oscillates, it will produce a varying electric and magnetic field at right angles to one another •these oscillating fields propagate as transverse waves Speed in free space=3.0x10⁸ms⁻¹ Wavelengths: Gamma:<10⁻¹¹ X-ray:10⁻⁹-10⁻¹¹ UV:10⁻⁹-10⁻⁷ Visible:10⁻⁷ Infrared:10⁻⁷-10⁻⁴ Microwave:10⁻⁴-10⁰ Radio:10⁰-10⁵ to get frequency: f=c/λ=3x10⁸/λ

Describe the nature of standing (stationary) waves.

•does not transfer energy •has variable amplitude •may have phase difference of 0, π and 2π

Describe the interchange between kinetic energy and potential energy during SHM.

•during SHM, provided there are no resistive forces, TOTAL ENERGY MUST REMAIN CONSTANT

State and apply Snell's law.

•experimental law of refraction sini/sinr=constant(refractive index) sinθ₁/sinθ₂=v₁/v₂=n₂/n₁ •refractive index for air is 1

Outline qualitatively how polarisation may be used in stress analysis.

•glass and some plastics become birefringent when placed under stress •when polarised white light is passed through stressed plastics and then analysed, bright coloured lines observed in regions of maximum stress.

Describe what is meant by polarised light.

•light is make up of oscillating electric and magnetic fields that are right angles to one another •they are transverse waves, both fields are right angles to the direction of propagation POLARISED: light in which the (electric) field vector vibrates in one plane only

Notes to make about SHM.

•the time period T does NOT depend on the amplitude A •not all oscillations are SHM

Describe the reflection and transmission of waves at a boundary between two media.

•when any wave meets the boundary between two different media it is partially reflected and partially transmitted REFLECTION: •law of reflection: i=r TRANSMISSION: •as it goes through different medias it will change direction, refracted •change of direction due to change in speed of wave

Describe what happens when there is a driving force put on an oscillation.

•when driving frequency first applied, combination of natural and forced oscillations occur producing complex TRANSIENT oscillations. Once amplitude of transient oscillations have a steady condition: →system oscillates at driving frequency →amplitude of force oscillations is fixed →overall result is that the energy of the system remains constant →the amplitude of the oscillations depends on: ➢ comparative values of natural frequency and driving frequency ➢amount of damping present

State the principle of superposition and explain what is meant by constructive interference and by destructive interference.

•when two waves of the SAME TYPE meet they interfere •resulting wave worked out using principle of super position PRINCIPLE: overall disturbance at any point at any time were the waves meet is the vector sum CONSTRUCTIVE INTERFERENCE: superposition of 2 or more waves that are in phase DESTRUCTIVE INTERFERENCE: superposition of two or more waves that are out of phase by exactly 180 degrees

Explain and discuss qualitatively the diffraction of waves at apertures and obstacles.

•when waves pass through apertures they tend to spread out •waves also spread around obstacles •diffraction becomes relatively more important when wavelength is large compared to size of aperture (or object) •wavelength needs to be same order of magnitude as aperture for diffraction to be noticeable •diffraction more important with smaller obstacles and thinner gap widths SEE NOTES FOR DIAGRAMS.

Describe the significance of resolution in the development of devices such as CDs and DVDs, the electron microscope and radio telescopes.

CDs and DVDs: high resolution laser may read more information ELECTRON MICROSCOPE: electrons travel with very short wavelength, producing a high resolution picture RADIOTELESCOPE: wavelength of radio waves very long requires large dish to receive high resolution data

Compare standing waves and travelling waves.

STANDING: •all points on the wave have different amplitudes •same frequency •all points between one node and the next node are in phase •energy is not transmitted TRAVELLING: •all points on wave have same amplitude •same frequency •all points along a wavelength have different phase •energy is transmitted

Discuss the modes of vibration of strings and air in open and in closed pipes.

The lowest-frequency mode is known either as the fundamental or as the first harmonic.

Solve problems on the Doppler effect for electromagnetic waves using the approximation Δf=f₀v/c

Approximation may be used only when v << c. C=speed of light in a vacuum=3×10⁸ Can be written as: ∆λ=λ₀v/c

Outline an example in which the Doppler effect is used to measure speed.

Blood-flow measurements and the measurement of vehicle speeds.

State and apply the conditions for constructive and for destructive interference in terms of path difference and phase difference.

CONSTRUCTIVE INTERFERENCE: in phase path difference=nλ DESTRUCTIVE INTERFERENCE: out of phase by exactly 180 degrees path difference=(n+½)λ FOR CONSTRUCTIVE OR DESTRUCTIVE INTERFERENCE TO OCCURE MUST BE COHERENT.

Describe the terms crest, trough, compression and rarefaction.

CREST: high point-amplitude of a transverse wave TROUGH: low point-amplitude of a transverse wave COMPRESSION: portion of high pressure in a longitudinal wave RAREFACTION: portion of low pressure in a longitudinal wave

Define the terms displacement, amplitude, frequency, period, wavelength, wave speed and intensity.

DISPLACEMENT: •measures change taken place as result of a wave passing particular point •distance (m) of a particle in a particular direction from its origin AMPLITUDE: •maximum displacement of a particle from its origin (mean position) •wave does not lose energy if amplitude constant FREQUENCY: •number of complete oscillations per unit time (Hz) PERIOD: •time (s) taken for one complete oscillation to occur WAVELENGTH: •shortest distance between two points in phase with one another along a wave WAVE SPEED: •speed of the transfer of energy of a wave •speed at which the wavefronts pass a stationary observer INTENSITY: •power per unit area of a wave •proportional to the square of the wave's amplitude

Define the terms displacement, amplitude, frequency, period and phase difference.

DISPLACEMENT: instantaneous distance of the moving object from its mean position (in a specific direction) (m) AMPLITUDE: maximum displacement from the mean position (m) FREQUENCY: number of oscillations completed per unit time (Hz) PERIOD: time taken for one complete oscillation. T=1/f (s) PHASE DIFFERENCE: measure of how "in step" different particles are. •If in phase, 2π (one complete cycle) •If out of phase, π (half a cycle)

State the Rayleigh criterion for images of two sources to be just resolved.

If two sources are just resolved, then the first minimum of one diffraction pattern is located on top of the maximum of the other diffraction pattern.

Describe examples of damped oscillations.

LIGHT DAMPING(under damped): resistive force so small so a small fraction of the total energy is removed HEAVY DAMPING (over damped): large resistive force, can completely prevent oscillations from occurring CRITICAL DAMPING: Intermediate value for resistive force such that the time taken for particle to return to zero displacement is minimum. The system returns to its equilibrium state as fast as possible without any oscillations

Describe refraction into more and less dense mediums.

MORE DENSE: towards normal LESS DENSE: away from normal

Apply the Doppler effect equations for sound.

MOVING SOURCE: f'=f[v/(v±u)] +away -towards MOVING OBSERVER: f'=f[(v±u)/v] +towards -away

Explain the Doppler effect by reference to wavefront diagrams for moving-detector and moving-source situations.

MOVING SOURCE: •towards, waves bunch up, higher frequency observed •away, waves spread out, frequency observed lower MOVING OBSERVER: •towards, frequency increases •away, frequency decrease

Apply the expressions for KE, total energy and for potential energy.

PE=total energy-KE

Explain the terms polariser and analyser.

POLARISER: Optical filter that passes light of a specific polarization and blocks waves of other polarisations ANALYSER: name given to that second polarizer that is oriented at 90° to the first polarizer.

Describe what is meant by the Doppler effect.

Perceived change in frequency of a wave due to the relative movement of the source or the observer.

State that progressive (travelling) waves transfer energy.

Progressive (travelling) waves transfer energy without any net motion of the medium the wave travels in.

Describe graphically the variation with forced frequency of the amplitude of vibration of an object close to its natural frequency of vibration.

SEE NOTES FOR DIAGRAM

Describe what is meant by an optically active substance.

Substance that rotates the plane of polarisation of light that passes through it. e.g. sugar solution

State what is meant by resonance.

System is subject to an oscillating force at exactly the same frequency as the natural frequency of oscillation of the system.

Describe and give examples of transverse and of longitudinal waves.

TRANSVERSE: direction of motion of energy transfer is perpendicular to the direction of motion (oscillations) of the medium; ex. light waves LONGITUDINAL: direction of motion of energy transfer is the same as the direction of motion of the medium; ex. sound waves

Describe diffuse reflection.

•when light is reflected from an uneven surface •single incidented ray scattered in all directions •this is how images are created

State and apply Brewster's law.

There is a particular angle (measured relative to the normal) at which the reflected ray is completely plane-polarized called Brewster's Angle. With the light incident at Brewster's angle, i=θ, we see that the refracted angle, r = 90- θ .Then: n=sini/sinr=sinθ/cosθ or n=tanθ, tanθ=n₁/n₂

Describe examples of resonance where the effect is useful and where it should be avoided.

USEFUL: •quartz oscillators •microwave generator •radio receivers •musical instruments AVOIDED: •vibrations in machinery •greenhouse effect

Describe a wave pulse and a continuous progressive (travelling) wave.

WAVE PULSE: single oscillation CONTINUOUS PROGRESSIVE WAVE: series of successive oscillations

Describe waves in two dimensions, including the concepts of wavefronts and of rays.

WAVEFRONT: collection of neighboring points on a wave that are in phase with one another RAY: line drawn perpendicular to the direction of energy transfer of the wave

Sketch the variation with angle of diffraction of the relative intensity of light emitted by two point sources that has been diffracted at a single slit.

WELL RESOLVED: distinct different maxima JUST RESOLVED: discernibly different maxima NOT RESOLVED: appears as one large maxima For a circular aperture, first minimum is at angle θ=1.22λ/b b=diameter of the the aperture For a slit, first minimum was at angle: θ=λ/b b=slit width EQUATIONS FOR PROBLEMS: •from the equations above, able to work out, wavelength, distance between two points (that are to be resolved) and the distance between the aperture and the points •In equations above, for slit equation, b is the distance between the aperture and the points, and λ becomes the separation between the points SEE NOTES FOR DIAGRAM TO EXPLAIN

Derive the formula θ=λb for the position of the first minimum of the diffraction pattern produced at a single slit.

for first minimum: bsinθ=λ sinθ=λ/b since angle small sinθ≈θ ∴θ=λ/b SEE NOTES FOR DIAGRAMS

Describe the ray diagram of a point source of light.

light set off in all directions

Solve problems involving standing waves.

resonant mode that has lowest frequency is called the fundamental or first harmonic f₀ NODE IS AT CLOSED END CLOSED AT BOTH ENDS: λ=2L/n f=nf₀ OPEN AT ONE END: λ=4L/n f=nf₀ n is always odd OPEN AT BOTH ENDS: λ=2L/n f=nf₀

Explain what is meant by the expression "able to rotate the plane of polarization of light" for liquid crystals.

the liquid crystal changes the plane in which (electric) field vector rotates

Derive and apply the relationship between wave speed, wavelength and frequency.

v=distance/time=λ/T since 1/T=f v=fλ

Apply the equations v=v₀sinωt, v=v₀cosωt, v=±w√(x₀²-x²), x=x₀cosωt and x=x₀sinωt as solutions to the defining equation for SHM.

x₀=amplitude v₀=Aω a=-Aω²sinωt IMPORTANT: ω²=k/m k=resorting force per unit displacement m=oscillating mass MAX VELOCITY=ωx₀

Describe an oscillation.

•An object continually moving to and fro about a fixed average point (the mean position). • involve the interchange of energy between kinetic and potential

Describe Huygens' principle.

•Every point on a wavefront acts as a source of secondary circular wavelets •in the forward direction (θ=0) these are all in phase so they add up to give a maximum

Describe the use of polarization in the determination of the concentration of certain solutions.

•For a given optically active solution, the angle θ through which the plane of polarisation is rotated is proportional to: →the lenght of the solution →the concentration of the solution •A polarimeter is a device that measures θ →consists of two polariser (a polariser and an analyser) that are initially aligned →solution is introduced between two and analyser is rotated to find the maximum transmitted light

State what is meant by damping.

•It is a dissipative, frictional force that acts on an oscillation in the opposite direction to the direction of movement of the oscillating particle. •It does work against this resistive (or dissipative force) so the particle loses energy. •amplitude will decrease exponentially with time

Describe polarization by reflection.

•Light incident upon certain materials, may be totally or partially polarized. •Consider windows on the Metro train at night. -The passenger inside can see their reflection in the glass but also a person outside can see the passenger inside -This must mean that some of the light is transmitted/refracted while some of it is reflected •This reflected light is in fact polarised. •θi+θr=90°

Define simple harmonic motion (SHM) and state the defining equation.

•The acceleration of an object is always directed towards and is proportional to its displacement from a fixed point. •acceleration is caused by a restoring forces F∝-x, since F=ma, a∝-x •the negative sign signifies the acceleration is always directed back towards its mean position a=−ω²x ω is the angular frequency USE THIS FOR SPRINGS UNDERGOING SHM

State what is meant by natural frequency of vibration and forced oscillations.

NATURAL FREQUENCY: natural oscillations of particles without external forces FORCED OSCILLATIONS: •force a system to oscillate at a frequency •natural oscillation subject to a changing force that varies with chosen frequency, and is provided from outside the system

Define nodes and antinodes.

NODES: midpoint of each wave wherein destructive interference occurs (zero displacement) ANTINODES: point where constructive interference occurs (maximum displacement)

Explain the formation of one-dimensional standing waves.

OCCURS WHEN TWO WAVES MEET THAT ARE: →of the same amplitude →of the same frequency →travelling in opposite direction →in the same medium •often occurs when wave bounces back from a boundary along the route it came