Anatomy of a wave
A wave is a traveling disturbance that carries energy without carrying stuff along with it. Ocean buoys rise and fall but never cross the sea — the wave's energy does. Two families cover everything: transverse waves wiggle perpendicular to the direction of travel (light, stadium waves), while longitudinal waves wiggle parallel to travel, squeezing and stretching the medium (sound).
Learn the parts on a transverse wave sketch: crests (tops), troughs (bottoms), wavelength λ (crest-to-crest distance), amplitude (height from the resting position to a crest) and frequency f (how many waves pass a point each second, in hertz). Amplitude is energy's volume knob; wavelength and frequency are its identity.
- Crest = top · Trough = bottom
- Wavelength (λ): distance from crest to crest (or trough to trough)
- Amplitude: height away from the rest position — bigger = more energy
- Frequency (f): waves per second, in hertz (Hz)
- Transverse wiggles sideways (light); longitudinal squeezes forward (sound)
Frequency, pitch and the wave equation
For sound, frequency is pitch: high f = squeaky, low f = rumble. Humans hear roughly 20 Hz to 20,000 Hz, and dogs comfortably beat the top of that range. Amplitude is loudness — a stronger swing carries more energy to your eardrum.
All waves obey one equation: v = f × λ — wave speed equals frequency times wavelength. For sound in room-temperature air, v ≈ 343 m/s no matter what's playing, so a higher frequency automatically comes with a shorter wavelength. Frequency is set by the source; speed is set by the medium.
- v = fλ: speed (m/s) = frequency (Hz) × wavelength (m)
- High frequency = high pitch; amplitude = loudness
- Sound in air travels about 343 m/s
- Period T = 1/f — seconds per wave
A violin plays A above middle C at 440 Hz. In air, v = fλ → 343 = 440 × λ, so λ = 343 ÷ 440 ≈ 0.78 m. Doubling the frequency to 880 Hz halves the wavelength to about 0.39 m — frequency and wavelength always trade off like this in the same medium.
The Doppler effect, echoes and silent space
The Doppler effect: when a wave source moves toward you, each wave crest starts slightly closer than the last, so they arrive more often — higher frequency, higher pitch. Moving away stretches the waves — lower pitch. The ambulance siren's slide as it passes is the classic demo, and race cars and redshifted galaxies play the same trick.
Sound needs a medium — something to squeeze — which is why space battles are silent no matter what movies say. Echoes are reflections: sonar and bats time the echo's round trip and divide, using distance = (speed of sound × time) ÷ 2.
- Source moving toward you → waves bunch → higher pitch
- Source moving away → waves stretch → lower pitch
- Sound needs a medium: no air, no sound
- Echo ranging: distance = (speed of sound × time) ÷ 2
- Light does it too: galaxies moving away look redder (redshift)
Key concepts to memorize
🎯 Study tips for this topic
- Sketch and label one wave per study session until crest, trough, λ and amplitude are automatic.
- Chant 'v equals f lambda' and practice the three rearrangements (f = v/λ, λ = v/f).
- Link each term to a sense: frequency = pitch, amplitude = loudness.
- Explain the Doppler effect to someone using a toy car and a hum — teaching it proves you know it.
- Use the flashcards for unit checks: Hz, m, m/s — units catch most wave-equation errors.
