๐Wave Properties
What is a Wave?
A wave is a disturbance that carries energy through a medium (or through empty space) without carrying matter along with it.
Types of waves: - Transverse waves: particles vibrate perpendicular to the direction of wave travel (light, string waves) - Longitudinal waves: particles vibrate parallel to the direction of wave travel (sound waves)
Key wave properties: - Amplitude (A): maximum displacement from equilibrium. Determines the energy/intensity of the wave. - Wavelength (ฮป): distance between two consecutive identical points (crest-to-crest or trough-to-trough). Measured in meters. - Period (T): time for one complete oscillation (s) - Frequency (f): number of oscillations per second (Hz = 1/s)
Wave Superposition
When two waves meet, they superpose (add together):
- Constructive interference: waves in phase โ amplitudes add โ bigger wave - Destructive interference: waves out of phase โ amplitudes subtract โ smaller (or zero) wave
After passing through each other, waves continue unchanged โ they don't permanently affect each other.
Wave Properties Visualization
See how amplitude and wavelength affect the wave shape. Two waves superposing shows interference.
๐ Key Equations
Wave properties
f = (1)/(T)v = fฮปE โ Aยฒ (energy proportional to amplitude squared)โ ๏ธ Common Mistakes
Misconception: Waves transport matter from one place to another.
โ Correct thinking: Waves transport energy, not matter. The medium's particles oscillate in place and return to equilibrium.
Why: Think of a wave on a rope: the rope itself doesn't travel along; only the disturbance (energy) moves forward.
Misconception: A larger amplitude means a higher frequency.
โ Correct thinking: Amplitude and frequency are independent properties. Amplitude controls energy; frequency controls pitch (for sound) or colour (for light).
Why: You can have a loud low-pitched sound (large amplitude, low frequency) or a quiet high-pitched sound (small amplitude, high frequency).
Misconception: Destructive interference destroys the energy of both waves.
โ Correct thinking: Destructive interference cancels displacement locally, but the energy is redistributed โ not destroyed.
Why: Energy is conserved. Where waves cancel (nodes), the energy appears elsewhere as kinetic energy or at antinodes.
๐ Practice Problems
Try these problems. Check your answer when ready.
A wave has a period of 0.02 s. What is its frequency?
f = 1/TA wave has a frequency of 200 Hz and a wavelength of 1.7 m. What is its speed?
Wave A has amplitude 3 cm and wave B has amplitude 6 cm. How do their energies compare?
E โ AยฒTwo identical waves with amplitude 5 cm superpose in phase. What is the amplitude of the resulting wave? If they superpose exactly out of phase?
A transverse wave on a rope has wavelength 0.4 m and period 0.1 s. What is the wave speed? If the amplitude is doubled, how does the speed change?
Finished reading through this lesson?