Transverse and longitudinal waves
A wave transfers energy (and information) from place to place without transferring matter. Two main types: transverse and longitudinal.
Transverse waves
- Particles oscillate perpendicular to the direction of energy travel.
- Examples: water surface waves, all electromagnetic waves (light, radio, etc.), waves on a stretched string.
Longitudinal waves
- Particles oscillate parallel to the direction of energy travel.
- Compressions (squeezed regions) and rarefactions (stretched regions).
- Examples: sound, ultrasound, P-waves in earthquakes.
Wave properties
- Amplitude ($A$) — maximum displacement from rest position. Larger A → more energy.
- Wavelength ($\lambda$) — distance between two consecutive crests or compressions. Unit: m.
- Frequency ($f$) — number of complete waves per second. Unit: hertz (Hz).
- Period ($T$) — time for one complete wave cycle. $T = 1/f$.
Wave equation
$v = f\lambda$
- $v$ — wave speed (m/s).
- $f$ — frequency (Hz).
- $\lambda$ — wavelength (m).
✦Worked example— Worked example 1
A water wave has $f = 2.0$ Hz and $\lambda = 0.50$ m. Find its speed.
- $v = f\lambda = 2.0 \times 0.50 = 1.0$ m/s.
✦Worked example— Worked example 2
A sound wave has $f = 440$ Hz (concert A). Speed of sound ≈ 340 m/s. Wavelength?
- $\lambda = v/f = 340/440 \approx 0.77$ m.
Why waves don't transfer matter
Particles oscillate about their rest position. They don't travel with the wave — they pass energy on to neighbours. Watch a stick in water: it bobs up and down but doesn't drift away with the wave.
Period from frequency
$T = 1/f$. So a 50 Hz signal has $T = 0.02$ s.
⚠Common mistakes
- Saying waves transfer matter — they don't, only energy.
- Reading wavelength as half a wave (it's full crest-to-crest).
- Confusing transverse and longitudinal — sound is longitudinal (compression).
- Forgetting units: f in Hz, λ in m, v in m/s.
AI-generated · claude-opus-4-7 · v3-deep-physics