Wave Properties and Relationships
Waves are characterized by wavelength (?), frequency (f), and velocity (v), related by v = f?. Wavelength is the distance between successive crests. Frequency is oscillations per second (Hz). Wave velocity depends on the medium. Sound in air travels at 343 m/s, while light in vacuum travels at 3x10? m/s. Period T = 1/f is the time for one complete oscillation. Angular frequency ? = 2pif appears in wave equations and relates frequency to radians.
Different Types of Waves
Mechanical waves require a medium (sound, water waves, seismic waves). Electromagnetic waves don't need a medium (light, radio, X-rays). Longitudinal waves oscillate parallel to propagation (sound), while transverse waves oscillate perpendicular (light, water). All waves carry energy and information. Higher frequency means more energy per photon in electromagnetic waves. Understanding wave properties is fundamental to acoustics, optics, telecommunications, and quantum mechanics.
Applications in Technology
Wave calculations are essential in modern technology. Radio stations broadcast at specific frequencies. WiFi uses microwaves around 2.4 or 5 GHz. Musical instruments produce sound waves with specific frequencies determining pitch-A440 means 440 Hz. Ultrasound imaging uses high-frequency sound waves. Fiber optics transmit light waves. Engineers design antennas to match wavelengths. Seismologists analyze earthquake waves. Understanding waves enables GPS, MRI, radar, sonar, and countless technologies shaping modern life.
Quick Tips
- Always verify units are consistent
- Use scientific notation for very large/small numbers
- Results are approximations — real conditions may vary
Frequently Asked Questions
They're inversely proportional: ? = v/f. For a given wave velocity, higher frequency means shorter wavelength. In light, blue has higher frequency and shorter wavelength than red.
Wave velocity depends on the medium's properties. Sound speed depends on air temperature and composition. Light speed in materials depends on refractive index. Water wave speed depends on depth.
Frequency is oscillations per second (Hz), while period is time per oscillation (seconds). They're reciprocals: f = 1/T. A 2 Hz wave has a 0.5-second period.
Angular frequency ? = 2pif converts frequency to radians per second. It's useful in wave equations and relates to circular motion. A 1 Hz wave has ? = 2pi rad/s.
Light color depends on wavelength/frequency. Visible light ranges from red (~ 700 nm, 430 THz) to violet (~ 400 nm, 750 THz). Our eyes perceive different wavelengths as different colors.