Last Minute Lecture

Electromagnetic Waves – Principles & Applications Explained | Chapter 32 of University Physics Chapter 32 unifies electricity and magnetism into the self-sustaining phenomenon of electromagnetic waves. We’ll explore how Maxwell’s equations predict wave propagation at the speed of light, the transverse nature of E and B fields, energy and momentum transport, standing wave formation, and real-world applications from radio to lasers. Watch the full video summary here for animated demonstrations of EM wave behavior. Maxwell’s Equations & Wave Generation Maxwell’s extension of Faraday’s and Ampère’s laws shows that time-varying E fields induce B fields and vice versa, forming a self-propagating wave. The wave speed in vacuum is: c = 1/√(ε₀ μ₀) ≈ 3.00×10⁸ m/s , matching the measured speed of light and confirming light as an electromagnetic wave. Plane Waves & Transverse Nature Electromagnetic waves are transverse: E and B oscillate perpendicular to each other and t...

Sound Waves – Properties, Behavior & Applications Explained | Chapter 16 of University Physics Chapter 16 explores how sound waves propagate through different media and manifest in phenomena like resonance, interference, beats, and the Doppler effect. You’ll learn the basics of longitudinal mechanical waves, how we measure and perceive them, and their critical applications in acoustics and engineering. Watch the full video summary here for detailed explanations and demonstrations. What Is a Sound Wave? Longitudinal wave: particles oscillate parallel to wave propagation. Audible range: 20 Hz to 20 kHz (infrasonic below, ultrasonic above). Phase relation: pressure and displacement are 90° out of phase. Pressure wave model: p(x, t) = B k A sin(kx – ωt). Speed of Sound In fluids: v = √(B/ρ), where B is bulk modulus. In solids: v = √(Y/ρ), with Y Young’s modulus. In gases: v = √(γRT/M), rising with temperature. Wavelength relation: λ = v/f. ...

Mechanical Waves – Propagation, Energy & Superposition Explained | Chapter 15 of University Physics Chapter 15 explores how mechanical waves transport energy through media without bulk matter motion. From transverse and longitudinal disturbances to standing wave patterns, this chapter provides the tools to model, analyze, and apply wave behavior across strings, air, and fluids. Watch the full video summary here for detailed derivations and real-world examples. Types of Mechanical Waves Transverse waves – Particle motion ⟂ wave direction (e.g., waves on strings). Longitudinal waves – Particle motion ∥ wave direction (e.g., sound in air). Surface waves – Combine transverse and longitudinal motion (e.g., water waves). Wave Parameters & Periodic Waves Key parameters describe any periodic wave: Amplitude (A): Maximum displacement from equilibrium. Wavelength (λ): Distance between repeating points. Frequency (f): Cycles per second, f = 1/T. P...