Flashcards · 9630 · AS Topic 5

Oscillations and waves (AS Level) flashcards

62 cards on AS Topic 5, subtopics 3.5.1 to 3.5.11. Pick a subtopic or study them all.

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3.5.1 Oscillating systems

Period and amplitude of an oscillation: Period T: the time taken by one full oscillation (f = 1/T). Amplitude: the maximum displacement from equilibrium.
Period of a mass-spring system and of a simple pendulum: Mass-spring: T = 2π√(m/k). Simple pendulum (small angles): T = 2π√(l/g), with l measured to the centre of the bob. Neither depends on amplitude; the pendulum does not depend on the bob's mass.
Damping: Energy is transferred from the oscillator to the surroundings by resistive forces, so the amplitude falls.
Light, critical and heavy damping: Light: oscillates with amplitude falling each cycle; period almost unchanged. Critical: returns to equilibrium in the shortest time without oscillating (e.g. car suspension). Heavy: no oscillation, slow return.
Required practical: finding g with a pendulum. Graph and timing technique: Vary l and time 10 oscillations, repeating. Plot T² against l: gradient = 4π²/g. Start and stop timing at the equilibrium position using a fiducial marker, where the bob moves fastest.
How do Ek and Ep vary during an undamped oscillation?: Ek is maximum at equilibrium and zero at maximum displacement; Ep the reverse. The total is constant. Against time, each goes through two cycles for every cycle of the motion.

3.5.2 Forced vibrations and resonance

Free vibration vs forced vibration: Free: displaced once, then left to oscillate at its natural frequency. Forced: driven by a periodic force, it vibrates at the driver's frequency.
Resonance: When the driving frequency equals the natural frequency, the amplitude is a maximum and the driver transfers energy to the system at its greatest rate.
Effect of increasing damping on a resonance curve: The peak is lower and broader, and occurs slightly below the natural frequency. Light damping gives a tall, sharp peak.
Two examples of resonance: Any two: a child on a swing pushed in time, a car panel rattling at one engine speed, footbridges swaying, musical instruments, stationary waves on strings and in air columns.
Lowest resonant frequency of a string fixed at both ends: f = v/2L, then 2f, 3f and so on. For L = 1.0 m and v = 50 m s⁻¹: 25 Hz, then 50 Hz.

3.5.3 Progressive waves

Progressive wave: A wave that transfers energy from one place to another without transferring the medium itself.
Wavelength, frequency and wave speed: Wavelength λ: distance between two adjacent points oscillating in phase. Frequency f: number of complete oscillations per second (Hz). Wave speed c = fλ.
Phase difference between two points a distance x apart on a wave: Phase difference = 2πx/λ radians (or x/λ cycles, × 360 for degrees). In phase: 0, 2π, 4π…; antiphase: π, 3π…
Points 0.45 m apart on a wave of wavelength 0.60 m: phase difference?: 0.45 ÷ 0.60 = 0.75 cycle = 270° = 3π/2 rad.
Ultrasound imaging: depth of a boundary from an echo: Depth = (speed × time delay) ÷ 2, because the pulse travels there and back. Gel removes the air gap, which would otherwise reflect most of the ultrasound.

3.5.4 Longitudinal and transverse waves

Transverse vs longitudinal waves: Transverse: oscillations perpendicular to the direction of energy transfer (string waves, all electromagnetic waves). Longitudinal: oscillations parallel to the direction of energy transfer, with compressions and rarefactions (sound).
Plane-polarised wave: A wave whose oscillations are confined to a single plane that contains the direction of travel.
What does polarisation show about light, and why can sound not be polarised?: Only transverse waves can be polarised, so polarisation is evidence that light is transverse. Sound is longitudinal, so it cannot be polarised.
Unpolarised light passes through two Polaroids. What happens as the second is rotated through 360°?: Two maxima (axes parallel) and two minima, with almost no light when the axes are crossed at 90°.
How should a receiving rod aerial be aligned?: Parallel to the transmitting aerial (along the plane of the electric field) for the strongest signal; at 90° the signal is nearly zero.
Speed of all electromagnetic waves in a vacuum: 3.00 × 10⁸ m s⁻¹. They are oscillating electric and magnetic fields, perpendicular to each other and to the direction of travel, and need no medium.

3.5.5 Principle of superposition of waves and formation of stationary waves

Principle of superposition: Where waves meet, the resultant displacement is the sum of their separate displacements (taking signs into account).
How is a stationary wave formed?: Two waves of the same frequency (and similar amplitude) travelling in opposite directions, often a wave and its reflection, superpose. It has fixed nodes and antinodes and transfers no energy along its length.
Node and antinode: Node: a point of zero amplitude, where the two waves are always in antiphase. Antinode: a point of maximum amplitude, where they are always in phase.
Node-to-node and node-to-antinode distances: Node to node = λ/2. Node to adjacent antinode = λ/4.
First harmonic frequency of a stretched string: f = (1/2l)√(T/μ), where l is the vibrating length, T the tension and μ the mass per unit length. The nth harmonic has n loops and frequency nf₁.
Stationary vs progressive wave: phase of points: Stationary: all points within one loop are in phase; points in adjacent loops are in antiphase. Progressive: phase changes continuously along the wave.

3.5.6 Interference

Coherent sources: Sources with the same frequency and a constant phase difference.
Path difference for constructive and destructive interference (coherent sources in phase): Constructive (bright, loud): path difference = nλ. Destructive (dark, quiet): path difference = (n + ½)λ.
Young's double slit fringe spacing equation: w = λD/s, where s is the slit separation and D the slit-to-screen distance (D much greater than s).
Effect on double-slit fringe spacing of increasing λ, s and D: Longer λ: wider spacing. Greater slit separation s: narrower spacing. Greater screen distance D: wider spacing.
Laser safety in an interference practical: Use a low-power laser, never look into the beam or at a shiny reflection, and stop the beam at the end of its path with a matt surface.
Double-slit pattern with white light: A white central fringe, with coloured fringes either side: blue on the inner edge, red on the outer.

3.5.7 Diffraction

Diffraction: The spreading of a wave as it passes through a gap or around an edge.
Single-slit diffraction: what affects the width of the central maximum?: A narrower slit or a longer wavelength gives a wider central maximum; a wider slit gives a narrower one.
Diffraction grating equation: d sin θ = nλ, where d is the slit spacing (1 ÷ lines per metre), n the order and θ measured from the straight-through direction.
How do you find the highest order a grating can produce?: Since sin θ cannot exceed 1, n ≤ d/λ, rounded down to a whole number. Total maxima = 2n + 1.
Grating with 200 lines per mm: what is d?: d = 1 ÷ (200 × 10³ m⁻¹) = 5.00 × 10⁻⁶ m.

3.5.8 Refraction at a plane surface

Refractive index of a substance: n = c/c_s, the speed of light in a vacuum ÷ the speed in the substance. No unit; n of air ≈ 1.
Snell's law: n₁ sin θ₁ = n₂ sin θ₂, with angles measured from the normal.
Critical angle: equation and condition for total internal reflection: sin θc = n₂/n₁ (n₁ > n₂). TIR happens when light travels towards a medium of lower refractive index and the angle of incidence exceeds θc.
Step-index optical fibre: role of the cladding: It has a lower refractive index than the core, so TIR happens at the core boundary. It also protects the core surface, prevents cross-talk between fibres and adds strength.
Modal vs material dispersion in an optical fibre: Modal: rays take different paths, so arrive at different times; reduced by a narrow (single-mode) core. Material: n depends on wavelength, so different wavelengths travel at different speeds; reduced by monochromatic light.
Absorption vs pulse broadening in a fibre: Absorption reduces the amplitude (power) of a pulse. Dispersion broadens (lengthens) it, so pulses can overlap, which limits the data rate.

3.5.9 Collisions of electrons with atoms

Electronvolt: The energy gained by an electron accelerated through a p.d. of 1 V: 1 eV = 1.60 × 10⁻¹⁹ J.
Excitation vs ionisation: Excitation: an electron in an atom moves to a higher energy level. Ionisation: an electron is removed from the atom.
Exciting an atom: colliding electron vs photon: A free electron can excite the atom if its kinetic energy is at least the energy gap; it keeps the surplus. A photon is absorbed only if its energy exactly equals a gap.
What do line spectra show, and what is the photon energy for a transition?: Only certain frequencies appear, so atomic energy levels are discrete. Photon energy hf = E₁ − E₂, the difference between the two levels.
How does a fluorescent tube produce visible light?: Accelerated electrons collide with mercury atoms and excite them. De-excitation emits ultraviolet photons, which the phosphor coating absorbs and re-emits as visible light.
Shortest X-ray wavelength from a tube at p.d. V: An electron gives all its energy eV to one photon: λmin = hc/eV.

3.5.10 Photoelectric effect

Work function and threshold frequency: Work function ϕ: the smallest energy an electron needs to escape the metal surface. Threshold frequency f₀: the lowest frequency that releases photoelectrons. ϕ = hf₀.
Photoelectric equation: hf = ϕ + Ek(max).
Stopping potential: The reverse p.d. that just stops the fastest photoelectrons: eVs = Ek(max).
Why does light below the threshold frequency release no electrons, however intense?: One photon gives all its energy to one electron. If hf < ϕ, no single electron gets enough energy to escape; more intense light only means more such photons.
Effect of intensity and of frequency on photoemission (above f₀): Greater intensity: more photoelectrons per second (larger current). Higher frequency: greater maximum kinetic energy.
Graph of stopping potential against frequency: what do the gradient and intercept give?: Gradient = h/e, so h = gradient × e. The intercept on the frequency axis is f₀.

3.5.11 Wave-particle duality

de Broglie wavelength: λ = h/p = h/mv, the wavelength associated with a particle of momentum p.
Evidence for wave-particle duality: Electron diffraction shows particles behaving as waves. The photoelectric effect shows electromagnetic waves behaving as particles.
When is electron diffraction noticeable?: When the de Broglie wavelength is about the same size as the gap or atomic spacing. Greater momentum gives a shorter wavelength and less diffraction.
de Broglie wavelength of an electron accelerated through p.d. V: Ek = eV, p = √(2mEk), λ = h/p.
Why do large everyday objects show no wave behaviour?: Their momentum is so large that λ = h/p is negligible compared with any gap they could pass through.