General Wave Characteristics
High-Yield Summary
- Transverse waves oscillate perpendicular to travel direction (EM waves, water surface); longitudinal waves oscillate parallel to travel direction, forming compressions/rarefactions (sound).
- Core relationships: T = 1/f, ω = 2πf, v = fλ. Amplitude (A) sets energy carried, not speed.
- Superposition: overlapping waves' displacements add. In-phase overlap → constructive interference (bigger amplitude); out-of-phase overlap → destructive interference (reduced/zero amplitude).
- Standing waves form when two same-frequency, same-amplitude waves travel in opposite directions and interfere at fixed points — nodes (zero displacement) and antinodes (max displacement), no net energy transfer.
- Resonance: a periodic driving force matching an object's natural frequency dramatically amplifies oscillation; damping dissipates energy over time and limits amplitude growth.
Transverse vs. Longitudinal Waves
| Transverse | Longitudinal |
|---|---|
| Particle motion perpendicular to travel direction | Particle motion parallel to travel direction |
| Pattern: crests and troughs | Pattern: compressions and rarefactions |
| Examples: EM waves, water surface waves | Example: sound waves |
Period, Angular Frequency, and Wave Speed
T = 1/f, ω = 2πf, v = fλ
- T = Period — time for one full cycle
- f = Frequency, in hertz (Hz = cycles/s)
- ω = Angular frequency, in rad/s
- v = Wave speed
- λ = Wavelength — distance between two consecutive in-phase points
- Worked example: f = 5 Hz, λ = 2 m → v = fλ = 10 m/s.
- If frequency increases while λ stays constant, wave speed must increase.
Constructive vs. Destructive Interference
| Constructive | Destructive |
|---|---|
| In phase (peaks align with peaks) | Out of phase (peak aligns with trough) |
| Resultant amplitude larger than either wave | Resultant amplitude reduced, possibly to zero |
| e.g., louder sound from aligned waves | e.g., noise-canceling headphones |
Key Terms
- Phase difference
- How aligned two overlapping waves are — in phase (peaks/troughs match) or out of phase (peak meets trough).
- Traveling wave
- Moves continuously through a medium, transferring energy along its path.
- Standing wave
- Two same-frequency/amplitude waves traveling opposite directions interfere to form a stationary pattern — oscillates in place, no net energy transfer.
- Node
- Point on a standing wave with zero displacement.
- Antinode
- Point on a standing wave with maximum displacement.
- Natural frequency
- The frequency an object tends to oscillate at when disturbed, set by its size/shape/material.
- Resonance
- Amplitude dramatically increases when a periodic driving force matches an object's natural frequency.
- Damping
- Friction/air resistance/internal losses that gradually reduce oscillation amplitude over time.
Common MCAT Trap
- Standing waves do not transfer energy through the medium — don't treat them like traveling waves when asked about energy transport.
- A reflected wave off a fixed boundary comes back phase-inverted — factor this in when predicting interference patterns at a fixed end.
- Amplitude affects energy/loudness, not wave speed — don't confuse the two when a question changes amplitude but asks about speed.
Quick Recall
A wave has f = 10 Hz and λ = 0.5 m. What is its speed?
Two identical waves overlap perfectly out of phase. What happens to the resultant amplitude?
Why don't standing waves transfer energy across space?