IB PHYSICS Topic 4: Oscillations and Waves

Periodic Motion

Motion that repeats itself after equal intervals of time.

Amplitude (A)

Maximum displacement from the equilibrium position.

Time period (T)

Time taken for a complete oscillation.

Frequency (f)

Number of oscillations per unit time. (f = 1/T)

Angular frequency (𝓌)

Equivalent of frequency. (𝓌 = 2(π)f)

Phase (θ)

If the motion starts away from equilibrium, it leads or lags by θ.

Isochronous oscillations

Maintain a constant time period regardless of amplitude changes.

Simple Harmonic Motion (SHM)

A type of periodic motion where the restoring force is proportional to the negative displacement from the equilibrium position.

Equation defining SHM

a - kx where a is accelerated, k is a constant, and x is displacement.

Velocity (v)

v = (dx)/(dt) = 𝓌Acos(𝓌t + θ)

Acceleration(a)

a = (dv)/(dt) = -𝓌^2(A)(sin(𝓌t+θ))

Wavefront

A surface perpendicular to the direction of wave travel.

Wavelength (⅄)

Shortest distance between two points in phase on a wave.

Period (T)

Time for a complete wavelength to pass a fixed point.

Frequency (f)

Number of wavelengths passing through a fixed point per unit time.

Transverse waves

Direction of vibration perpendicular to the direction of propagation.

Longitudinal waves

Direction of vibration parallel to the direction of propagation.

Wave Equation

The velocity of a wave (c) is given by c = f⅄

Intensity (I)

Power received per unit area. I = (P)/(4πr^2) and is proportional to the square of amplitude (A^2).

Principle of Superposition

When two waves meet, the total displacement is the vector sum of their individual displacements.

Polarization

Restriction of oscillation direction to a plane perpendicular to the direction of propagation. Result:Plane-polarized light.

Malus’s Law

Intensity (I) transmitted by an analyzer is proportional to cos^2(θ) where θ is the angle between the polarizer and the analyzer.

Laws Of Reflection And Refraction

Incident, reflected, and refracted rays, and normal lie on the same plane. The angle of incidence equals the angle of reflection. (sinθ1)/(sinθ2) = 1/n (Snell’s Law)

Critical Angle And Total Internal Reflection

The angle of incidence for which the angle of refraction reaches the right angle is the critical angle. Total internal reflection occurs when the angle of incidence is greater than the critical angle.

Double-Slit Interference

Two coherent sources create interference patterns. Constructive interference occurs at nλ and is destructive at (n + ½)λ.

Diffraction

Wave passed through a narrow gap forms bright and dark fringes. Angular position of minima given by θ = (nλ/a).

Interference With Multiple Slits

More slits result in sharper and more intense maxima and minima.

Dispersion

Different wavelengths of light refract at different angles. White light disperses into its constituent wavelengths.

Resolution

Rayleigh's criterion states two points are just resolved if the central maximum of the first point falls on the first minimum of the second point.

Diffraction Grating

For a grating with N slits, R = λ/change in λ = mN

Reflection Of Light Off Thin Films

Reflected light undergoes a phase change of 180∘ if reflected off a denser medium. A thin film of thickness t, refractive index n, and incident wavelength λ exhibits interference.

Doppler Effect In Light

The change in frequency of the light wave is (v/c)(f_0).

Water Waves

Follow laws similar to light. Exhibit reflection, refraction, interference, and diffraction.

Wave Propagation

Wavefront consists of infinite new disturbance centers. Successive wavefronts result from wavelets from these disturbances.

Reflection Of Water Wave

When a wave hits a barrier, it behaves as if a similar wave is coming from the barrier in the opposite direction.

Doppler Effect In Sound

The frequency of a moving source changes for an observer at rest or moving toward/away from the source.

Standing Waves

Formed when two waves of equal amplitude and frequency traveling in opposite directions are superimposed. Positions of crests and troughs do not change with time.

Nodes and