Physics 2 — Momentum & Waves

Waves

continues from lesson 3 — values defined earlier in the course stay live here

wave anatomy — amplitude A, wavelength λ, crest and trough

ELI5: a wave carries energy without carrying matter (the cork bobs, the wave moves on). One bookkeeping rule ties it together: v = f·λ. The medium sets the speed; the source sets the frequency; so the wavelength is whatever's left over.

v_{sound} := 343 m/s

= 343 m / s speed of sound, room temperature

f_{A4} := 440 Hz

= 440 Hz concert pitch A

\lambda_{A} = \frac{v_{sound}}{f_{A4}}

= 0.77955 m about 78 cm crest to crest

A guitar string only sustains waves that fit — whole numbers of half-wavelengths. Those are the harmonics, and they are why a plucked string has a definite pitch.

L_{string} := 0.65 m

= 0.65 m scale length

v_{string} := 430 m/s

= 430 m / s wave speed on the string (tension & gauge set this)

f_{1} = \frac{v_{string}}{2 \cdot L_{string}}

= 330.77 Hz fundamental — about E₃ on a guitar

f_{2} = 2 \cdot f_{1}

= 661.54 Hz second harmonic: the octave

Real-world hook: v = f·λ explains why thunder lags lightning, how MRI and ultrasound image the body, and why a fire-truck siren drops in pitch as it passes (the Doppler effect).

Try it yourself: sound travels at 343 m/s. What is the wavelength of a 512 Hz tone? (v = f·λ.)

\lambda _{you} := 343 m/s / 512 Hz

= 0.66992 m ✏️ Your turn: find the wavelength. The check verifies f·λ = v = 343 m/s — so you must solve for λ.

✓ pass

abs(\lambda _{you} * 512 Hz - 343 m/s) < 0.01 m/s

green when frequency × wavelength = the wave speed

Where next: Physics 3 — the electric and magnetic fields, and the light that is both.