AP Physics 2: Comprehensive Review Notes on Waves, Sound, and Light

Waves

• Key Types of Waves

  • Transverse Waves: Medium moves perpendicular to the direction of the wave (e.g., electromagnetic waves like light).

  • Longitudinal Waves: Medium moves parallel to the direction of the wave (e.g., sound waves).

• Wave Pulse vs Wave Train

  • Wave Pulse: Single disturbance transferring energy without moving matter.

  • Wave Train: Continuous, periodic disturbance with defined wavelength and frequency.

• Universal Wave Equation

  • Wave speed ($v$) is a fundamental concept in wave physics.

• Energy of a Wave

  • Energy increases with amplitude, includes both kinetic and potential energy components (not required for AP Exam).

• Medium and Wave Speed

  • Mechanical waves (e.g., sound) require a medium; speed influenced by medium properties.

  • Electromagnetic waves (e.g., light) can propagate through a vacuum but are affected by the medium.

• Wave Speed on Strings

  • Two speeds:

  1. String speed (vibrates up and down).

  2. Wave speed (how fast the disturbance travels along the string).

• Fractions and Variables

  • $x$: Position along wave propagation direction

  • y: Displacement from equilibrium position.

• Simple Harmonic Motion

  • Displacement functions given as $x(t)$ and $y(x)$.

• Waveform Equations:

  • Temporal Wave Equation:

  • $x(t) = A ext{cos}( ext{wt})$

  • Can be further expanded to include frequency: $A ext{cos}(2 ext{π} ft)$.

  • Spatial Wave Equation:

  • $y(x) = A ext{cos} (kx)$; $k$ being the wave number.

• Phase Shift

  • Reflective surfaces cause phase shifts; critical for understanding interference patterns.

• Harmonics on Strings

  • Fundamental Frequency (First Harmonic): One antinode at the center of the string.

  • Higher Harmonics: E.g., second harmonic has 2 antinodes, fourth harmonic has 4 antinodes.

  • Each harmonic obeys the relationship $fn = nf1$.

• Wavelength Relationships:

  • Relationships between length of string and harmonics:

  • For fundamental:
    $rac{λ_1}{2} = L$

  • Where $L$ is string length.

Sound Waves

• Sound Propagation

  • Sound needs a medium (e.g., air, water).

  • Sound is a longitudinal wave characterized by compressions and rarefactions.

• Key Sound Properties:

  • Speed: Affected by medium density and temperature. Faster in solids than liquids than gases.

  • Pitch and Amplitude: Frequency affects pitch; amplitude affects volume.

• Doppler Effect:

  • Observed frequency changes based on observer's movement relative to the source.

  • Higher frequency when approaches, lower when moves away.

• Sound Interference:

  • Constructive interference increases sound intensity, destructive decreases.

Light Waves and Optics

• Electromagnetic Nature: Light is an electromagnetic wave, behaves both as a particle and wave.

• Reflection and Refraction:

  • Different materials affect the speed of light; thus, bending during refraction.

  • Snell's Law: $n<em>1 ext{sin}(θ</em>1) = n<em>2 ext{sin}(θ</em>2)$.

• Polarization:

  • Light can be polarized, affecting how light waves are absorbed or transmitted through materials.

• Thin Film Interference:

  • Light reflecting from boundaries of thin films can produce colorful patterns based on the film's thickness and the angle of reflection.

• Diffraction:

  • Bending of waves around obstacles resulting in an interference pattern.

• Spectroscopy via Diffraction Gratings:

  • Light sources can be analyzed using diffraction gratings for spectral lines.

Equations Summary

• Universal wave equation: $v = f \lambda$
  

• Snell's Law: $n<em>1 \sin(\theta</em>1) = n<em>2 \sin(\theta</em>2)$
  

• Wave equation applications, positions of maxima/minima with slits:
  

• Bright fringes: $d \sin(\theta) = m\lambda$
  

• Dark fringes: $d \sin(\theta) = \left(m + \frac{1}{2}\right)\lambda$
  

• Thin Film Interference Equations:
  

• Constructive: $2d = m\lambda$
  

• Destructive: $2d = \left(m + \frac{1}{2}\right)\lambda$