Waves

• What Can You Use Instead of the Time-Averaged Poynting Vector?
  For periodic fields, use the cycle-averaged Poynting vector; for pulses, integrate instantaneous flux over time. The right choice depends on what you need.
• How Do Mirrors Work?
  Mirrors reflect light because charges in their surfaces respond to incoming electromagnetic waves and emit fields that form a reflected wave.
• Can a Monochromatic Pulse Exist?
  A strictly monochromatic wave cannot be a finite pulse: localization in time requires a range of frequencies, though that range can be very narrow.
• Could Submarine Sonar Kill a Diver?
  A submarine’s active sonar could harm a diver at close range, but ordinary sonar is not known as a reliable way to kill one.
• What Is Constructive Interference of Electromagnetic Waves?
  Constructive interference occurs when coherent electromagnetic fields arrive in phase; learn how phase, path difference, polarization, and amplitude determine intensity.
• What Are the Applications of the Wave Equation?
  The wave equation models how disturbances travel. Explore its uses in strings, sound, light, water, and seismic waves, with a worked string example.
• What Is the Difference Between a Particle and a Wave?
  A particle is localized; a wave is a spreading disturbance. Learn the classical difference and why quantum objects show both particle-like and wave-like behavior.