Waves are all around us, from ocean swells to light beams. They transfer energy without moving matter, defined by properties like amplitude, wavelength, and frequency. Understanding these basics helps us grasp how waves behave and interact.

Waves come in different types: transverse, longitudinal, mechanical, and electromagnetic. Each type has unique characteristics, but they all follow the wave equation. This relationship between speed, frequency, and wavelength is key to understanding wave behavior and applications.

Wave Fundamentals

Properties of wave motion

• Wave motion transfers energy through medium without matter transfer
• Amplitude measures maximum displacement from equilibrium position
• Wavelength spans distance between consecutive crests or troughs
• Frequency counts waves passing fixed point per unit time
• Period measures time for one complete wave cycle
• Wave equation relates speed, frequency, wavelength: $v = f\lambda$

Transverse vs longitudinal waves

• Transverse waves oscillate perpendicular to wave direction (water waves, electromagnetic waves)
• Longitudinal waves oscillate parallel to wave direction (sound waves, spring compression waves)

Mechanical and electromagnetic waves

• Mechanical waves propagate through physical medium (sound, water, seismic waves)
• Electromagnetic waves travel without medium at light speed in vacuum (light, radio, X-rays)

Wavelength, frequency, and speed

• Wave speed remains constant in given medium
• Wavelength and frequency exhibit inverse relationship
• Higher frequency corresponds to shorter wavelength
• Wave equation: $v = f\lambda$
• Period inversely relates to frequency: $T = 1/f$

Superposition and wave interference

• Superposition principle: wave displacements add algebraically when meeting
• Constructive interference amplifies waves in phase (integer multiples of wavelength)
• Destructive interference diminishes waves out of phase (odd multiples of half-wavelength)
• Applications include standing waves in instruments, noise-canceling headphones, thin-film interference (soap bubbles)