Cambridge Pre-U Physics (Principal Subject) Syllabus

Distinguish between transverse and longitudinal waves, giving an example of each.

In a transverse wave, oscillations are perpendicular to the direction of energy transfer (e.g. light/EM waves, waves on a string). In a longitudinal wave, oscillations are parallel to energy transfer, producing compressions and rarefactions (e.g. sound).

What is the intensity of a wave and how does it relate to amplitude and distance from a point source?

Intensity is power per unit area: $I = \dfrac{P}{A}$. Intensity is proportional to amplitude squared, $I \propto A^{2}$, and for a point source obeys the inverse-square law $$I \propto \frac{1}{r^{2}}$$

Define polarisation and state which wave type can be polarised.

Polarisation restricts the oscillations of a wave to a single plane. Only transverse waves (e.g. light) can be polarised, because their oscillations are perpendicular to propagation; longitudinal waves cannot be polarised.

State the principle of superposition.

When two or more waves meet at a point, the resultant displacement equals the vector sum of the individual displacements at that point: $$y_{\text{total}} = y_1 + y_2 + \cdots$$

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

For two coherent sources: constructive interference occurs when path difference $= n\lambda$; destructive interference occurs when path difference $= \left(n + \tfrac{1}{2}\right)\lambda$, where $n = 0, 1, 2, \ldots$

Write the double-slit fringe-spacing equation and define each symbol.

$$w = \frac{\lambda D}{a}$$ where $w$ is the fringe spacing, $\lambda$ the wavelength, $D$ the slit-to-screen distance, and $a$ the slit separation.

Write the diffraction grating equation.

$$d\sin\theta = n\lambda$$ where $d$ is the grating spacing (distance between adjacent slits), $\theta$ is the angle of the $n$-th order maximum, and $n$ is the order number ($0, 1, 2, \ldots$).

What is meant by coherence, and why is it needed for a stable interference pattern?

Two sources are coherent if they maintain a constant phase difference (and have the same frequency). Coherence is required so that the interference pattern is stable and does not change with time.

Define simple harmonic motion (SHM) and give its defining equation.

SHM is oscillation where acceleration is proportional to displacement from equilibrium and directed toward it: $$a = -\omega^{2} x$$ where $\omega$ is the angular frequency.

For SHM, write the displacement, velocity, and maximum-speed equations (starting at maximum displacement).

$$x = x_0\cos(\omega t),\quad v = \pm\omega\sqrt{x_0^{2} - x^{2}},\quad v_{\max} = \omega x_0$$ where $x_0$ is the amplitude.

Give the period formulas for a mass-spring system and a simple pendulum.

Mass-spring: $$T = 2\pi\sqrt{\frac{m}{k}}$$ Simple pendulum: $$T = 2\pi\sqrt{\frac{L}{g}}$$

Describe the energy interchange in SHM and the total energy.

Energy continuously interchanges between kinetic and potential. KE is maximum at equilibrium ($x=0$) and zero at amplitude; PE is maximum at amplitude and zero at equilibrium. The total energy is constant: $E = \tfrac{1}{2}m\omega^{2}x_0^{2}$.

Distinguish between free, damped, and forced oscillations, and define resonance.

Free oscillation: at the natural frequency with no external force or damping. Damped: amplitude decreases over time due to energy loss. Forced: driven by a periodic external force. Resonance occurs when the driving frequency equals the natural frequency, giving maximum amplitude.

How does the speed of sound in air depend on its properties, and roughly what is its value?

Sound is a longitudinal mechanical wave; its speed depends on the medium's stiffness and density, increasing with temperature in a gas. In air at around $20^{\circ}\text{C}$ it is approximately $v \approx 340\ \text{m s}^{-1}$.

State the Doppler effect equation for a moving source and stationary observer.

$$f_{\text{obs}} = f_{\text{source}}\left(\frac{v}{v \pm v_s}\right)$$ Use $-$ when the source moves toward the observer (higher frequency) and $+$ when moving away (lower frequency); $v$ is the wave speed and $v_s$ the source speed.

State Ohm's law and define resistance.

For an ohmic conductor at constant temperature, current is proportional to potential difference: $V = IR$. Resistance $R = \dfrac{V}{I}$ is the opposition to current flow (unit: ohm, $\Omega$).

Give the formulas for combining resistors in series and in parallel.

Series: $$R_{\text{total}} = R_1 + R_2 + \cdots$$ Parallel: $$\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots$$

State Kirchhoff's two circuit laws.

Current law (conservation of charge): the sum of currents into a junction equals the sum out, $\sum I_{\text{in}} = \sum I_{\text{out}}$. Voltage law (conservation of energy): around any closed loop, $\sum \varepsilon = \sum IR$.

Define electromotive force (e.m.f.) and internal resistance.

E.m.f. ($\varepsilon$) is the energy transferred per unit charge by a source. Internal resistance ($r$) is resistance within the source. Terminal p.d.: $$V = \varepsilon - Ir$$

Give the formula for resistivity and three formulas for electrical power.

Resistivity: $$R = \frac{\rho L}{A}$$ Power: $$P = IV = I^{2}R = \frac{V^{2}}{R}$$

Define capacitance and give the energy stored in a capacitor.

Capacitance is charge stored per unit potential difference: $$C = \frac{Q}{V}$$ (unit: farad, $\text{F}$). Energy stored: $$E = \tfrac{1}{2}QV = \tfrac{1}{2}CV^{2} = \frac{Q^{2}}{2C}$$

Give the formulas for combining capacitors in series and in parallel.

Series: $$\frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots$$ Parallel: $$C_{\text{total}} = C_1 + C_2 + \cdots$$ (Note: opposite to resistors.)

Write the equation for the discharge of a capacitor through a resistor and define the time constant.

$$Q = Q_0\,e^{-t/RC}$$ The time constant is $\tau = RC$, the time for the charge to fall to $\dfrac{1}{e} \approx 37\%$ of its initial value. Voltage and current decay with the same exponential.

State Coulomb's law for the force between two point charges.

$$F = \frac{1}{4\pi\varepsilon_0}\frac{Q_1 Q_2}{r^{2}}$$ where $\varepsilon_0$ is the permittivity of free space and $r$ is the separation. The force is attractive for unlike charges and repulsive for like charges.

Give the electric field strength and potential due to a point charge.

Field strength: $$E = \frac{1}{4\pi\varepsilon_0}\frac{Q}{r^{2}}$$ Electric potential: $$V = \frac{1}{4\pi\varepsilon_0}\frac{Q}{r}$$ Field is a vector; potential is a scalar.

What is the electric field between two parallel plates, and define electric field strength generally?

Electric field strength is force per unit positive charge: $E = \dfrac{F}{Q}$ (unit $\text{N C}^{-1}$ or $\text{V m}^{-1}$). Between parallel plates the field is uniform: $$E = \frac{V}{d}$$

Give the formula for the magnetic force on a current-carrying conductor and on a moving charge.

On a wire: $F = BIL\sin\theta$. On a moving charge: $F = Bqv\sin\theta$, where $\theta$ is the angle between the velocity (or current) and the magnetic flux density $B$ (unit: tesla, $\text{T}$).

Describe the path of a charged particle moving perpendicular to a uniform magnetic field, and give the radius.

It moves in a circle because the magnetic force is always perpendicular to velocity, providing centripetal force. Setting $Bqv = \dfrac{mv^{2}}{r}$ gives $$r = \frac{mv}{Bq}$$

State Faraday's law and Lenz's law of electromagnetic induction.

Faraday's law: the induced e.m.f. is proportional to the rate of change of magnetic flux linkage, $\varepsilon = -\dfrac{d(N\Phi)}{dt}$. Lenz's law: the induced current opposes the change producing it (the minus sign), conserving energy. Flux $\Phi = BA$.

State the photoelectric equation and explain the work function.

$$hf = \phi + E_{k(\max)}$$ where $hf$ is the photon energy, $\phi$ is the work function (minimum energy to release an electron), and $E_{k(\max)}$ is the maximum kinetic energy of the emitted electron. Emission occurs only above the threshold frequency.

Write the de Broglie wavelength equation and the photon energy equations.

de Broglie wavelength: $$\lambda = \frac{h}{p} = \frac{h}{mv}$$ Photon energy: $$E = hf = \frac{hc}{\lambda}$$ demonstrating wave-particle duality.

Explain how line spectra arise and give the energy of an emitted photon.

Electrons occupy discrete (quantised) energy levels. When an electron drops from a higher level $E_2$ to a lower level $E_1$, it emits a photon: $$hf = E_2 - E_1$$ Each transition gives a specific wavelength, producing the line spectrum.

Define the unified atomic mass unit and write the mass-energy equivalence relation.

The unified atomic mass unit ($\text{u}$) is $\tfrac{1}{12}$ the mass of a carbon-12 atom, $\approx 1.66 \times 10^{-27}\ \text{kg}$. Mass-energy equivalence: $$E = mc^{2}$$ used to calculate binding energy and energy released in nuclear reactions.

Define binding energy and explain mass defect.

Binding energy is the energy required to separate a nucleus into its constituent nucleons. The mass defect $\Delta m$ is the difference between the mass of the nucleus and the sum of its nucleon masses; the binding energy is $E = \Delta m\, c^{2}$. Higher binding energy per nucleon means a more stable nucleus.

State the radioactive decay law and define the decay constant and half-life.

$$N = N_0\,e^{-\lambda t}$$ where $\lambda$ is the decay constant (probability of decay per unit time). Half-life is the time for half the nuclei to decay: $$t_{1/2} = \frac{\ln 2}{\lambda}$$ Activity $A = \lambda N$.

Compare nuclear fission and nuclear fusion.

Fission: a heavy nucleus splits into lighter nuclei, releasing energy (e.g. uranium in reactors). Fusion: light nuclei combine into a heavier nucleus, releasing more energy per nucleon (e.g. hydrogen in stars). Both release energy because the products have higher binding energy per nucleon.

Write the formulas linking pressure, volume, temperature for an ideal gas (equation of state).

$$pV = nRT = NkT$$ where $n$ is the number of moles, $R$ the molar gas constant, $N$ the number of molecules, and $k$ the Boltzmann constant ($k = R/N_A$).

State the relationship between the mean kinetic energy of a gas molecule and absolute temperature.

$$\langle E_k \rangle = \tfrac{3}{2}kT$$ The mean translational kinetic energy of a molecule is proportional to the absolute (kelvin) temperature; this defines temperature on a microscopic level.

Define specific heat capacity and specific latent heat.

Specific heat capacity: energy to raise unit mass by one kelvin, $Q = mc\Delta\theta$. Specific latent heat: energy to change the state of unit mass with no temperature change, $Q = mL$ (fusion for melting, vaporisation for boiling).

State the first law of thermodynamics.

The increase in internal energy of a system equals the heat added to it plus the work done on it: $$\Delta U = Q + W$$ This expresses conservation of energy for thermal systems.

State the Stefan-Boltzmann law and Wien's displacement law.

Stefan-Boltzmann (luminosity of a black body): $$L = 4\pi r^{2}\sigma T^{4}$$ Wien's law (peak wavelength): $$\lambda_{\max} T = \text{constant} \approx 2.9 \times 10^{-3}\ \text{m K}$$ Both relate a star's radiation to its surface temperature.

State Hubble's law and explain its significance.

$$v = H_0 d$$ where $v$ is a galaxy's recession velocity, $d$ its distance, and $H_0$ the Hubble constant. It shows the universe is expanding, with more distant galaxies receding faster — key evidence for the Big Bang.

Explain cosmological redshift and give the redshift formula.

Light from receding galaxies is stretched to longer (redder) wavelengths because space expands. Redshift: $$z = \frac{\Delta\lambda}{\lambda} \approx \frac{v}{c}$$ for $v \ll c$, where $\Delta\lambda$ is the change in wavelength.

Define the astronomical distance units: astronomical unit, light year, and parsec.

Astronomical unit (AU): mean Earth-Sun distance, $\approx 1.5 \times 10^{11}\ \text{m}$. Light year: distance light travels in one year, $\approx 9.5 \times 10^{15}\ \text{m}$. Parsec: distance at which $1\ \text{AU}$ subtends $1$ arcsecond, $\approx 3.1 \times 10^{16}\ \text{m}$.

State Newton's law of gravitation and the gravitational field strength of a point mass.

$$F = \frac{G m_1 m_2}{r^{2}}$$ Gravitational field strength (force per unit mass): $$g = \frac{GM}{r^{2}}$$ where $G$ is the gravitational constant. The force is always attractive.