🌊College Physics II – Mechanics, Sound, Oscillations, and Waves Unit 16 – Waves in Physics

Key Concepts and Terminology

• Waves transfer energy from one point to another without transferring matter
• Medium the material through which a wave propagates (water, air, solid)
• Crest the highest point of a wave
• Trough the lowest point of a wave
• Wavelength ($\lambda$) the distance between two consecutive crests or troughs
• Amplitude the maximum displacement of a wave from its equilibrium position
• Frequency ($f$) the number of wave cycles that pass a fixed point per unit time
• Period ($T$) the time required for one complete wave cycle ($T = 1/f$)

Types of Waves

• Mechanical waves require a medium to propagate (sound waves, water waves)
• Electromagnetic waves do not require a medium and can travel through a vacuum (light, radio waves, X-rays)
• Transverse waves the direction of oscillation is perpendicular to the direction of wave propagation (light waves, water waves)
• Longitudinal waves the direction of oscillation is parallel to the direction of wave propagation (sound waves, pressure waves)
  • Compressions regions of high pressure in a longitudinal wave
  • Rarefactions regions of low pressure in a longitudinal wave
• Surface waves travel along the interface between two media (ocean waves, seismic waves)

Wave Properties and Characteristics

• Speed ($v$) the rate at which a wave propagates through a medium ($v = \lambda f$)
• Phase the position of a point on a wave relative to its origin
• Dispersion the phenomenon where waves with different wavelengths travel at different speeds in a medium
• Polarization the orientation of the oscillations in a transverse wave
  • Linearly polarized waves oscillate in a single plane
  • Circularly polarized waves the direction of oscillation rotates as the wave propagates
• Intensity the power carried by a wave per unit area
• Attenuation the decrease in wave amplitude as it propagates through a medium

Mathematical Descriptions of Waves

• Wave equation a partial differential equation that describes the propagation of waves ($\frac{\partial^2 u}{\partial t^2} = v^2 \frac{\partial^2 u}{\partial x^2}$)
• Sinusoidal waves can be described by a sine or cosine function ($y(x,t) = A \sin(kx - \omega t + \phi)$)
  • $A$ amplitude
  • $k$ wavenumber ($k = 2\pi/\lambda$)
  • $\omega$ angular frequency ($\omega = 2\pi f$)
  • $\phi$ phase constant
• Complex exponential form a compact way to represent sinusoidal waves ($y(x,t) = Ae^{i(kx - \omega t)}$)
• Fourier analysis decomposing a complex wave into a sum of simple sinusoidal waves
• Dispersion relation relates the wavenumber to the angular frequency ($\omega = \omega(k)$)

Wave Behavior and Phenomena

• Reflection occurs when a wave encounters a boundary and bounces back
  • Specular reflection the angle of incidence equals the angle of reflection
  • Diffuse reflection the reflected wave scatters in many directions
• Refraction the change in direction of a wave as it passes from one medium to another
• Diffraction the bending of waves around obstacles or through openings
  • Huygens-Fresnel principle every point on a wavefront acts as a source of secondary wavelets
• Interference the superposition of two or more waves
  • Constructive interference waves in phase, resulting in increased amplitude
  • Destructive interference waves out of phase, resulting in decreased amplitude
• Standing waves a wave pattern that appears to be stationary, formed by the superposition of two identical waves traveling in opposite directions
  • Nodes points of no displacement in a standing wave
  • Antinodes points of maximum displacement in a standing wave

Applications in Physics and Engineering

• Acoustics the study of sound waves (musical instruments, noise reduction)
• Optics the study of light waves (lenses, mirrors, fiber optics)
• Seismology the study of seismic waves for understanding Earth's interior and predicting earthquakes
• Telecommunications using electromagnetic waves to transmit information (radio, television, cell phones)
• Medical imaging techniques that use waves to create images of the body (ultrasound, MRI)
• Quantum mechanics wave-particle duality and the probabilistic nature of particles (de Broglie wavelength)

Experimental Techniques and Observations

• Oscilloscopes devices that display the waveform of an electrical signal
• Interferometers instruments that use the principle of interference to make precise measurements (Michelson interferometer)
• Diffraction gratings surfaces with regularly spaced lines that cause light to diffract and form spectra
• Doppler effect the change in frequency of a wave observed when the source and observer are in relative motion
  • Redshift increase in wavelength (decrease in frequency) when the source and observer are moving apart
  • Blueshift decrease in wavelength (increase in frequency) when the source and observer are moving closer
• Spectroscopy the study of the interaction between matter and electromagnetic radiation (absorption, emission, scattering)

Connections to Other Physics Topics

• Simple harmonic motion the oscillatory motion of a system where the restoring force is proportional to the displacement (springs, pendulums)
• Resonance the phenomenon where a system oscillates with greater amplitude at specific frequencies
• Doppler effect and special relativity the relativistic Doppler effect accounts for time dilation at high velocities
• Waves and thermodynamics the connection between heat transfer and electromagnetic waves (blackbody radiation)
• Quantum mechanics the wave nature of particles (matter waves) and the uncertainty principle
• Electromagnetism the relationship between electric and magnetic fields in electromagnetic waves (Maxwell's equations)