WAV-01

Harmonic wave speed

v = f λ = ω / k.

Reading speed

Travelling wavesd'Alembert 1747

Governing equation

v=f\lambda=\omega/k

$f \in \left[1, 20000\right]$

where

f: Frequency (Hz)
\lambda: Wavelength (m)
v: Phase speed (m/s)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

v=f\lambda=\omega/k

$f \in \left[1, 20000\right]$

$f = 1$ $v = 0.78$

Along the curve

②

Domain of the variable — blue

f_{\min} = 1,\quad f_{\max} = 20000

$f \in \left[1, 20000\right]$

$f = 1$ $f = 1$

Along the curve

③

Response curve — green

v=f\lambda=\omega/k

$f \in \left[1, 20000\right]$

$f = 1$ $v = 0.78$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}v}{\mathrm{d}f}

$f \in \left[1, 20000\right]$

$f = 126.8$ $v^{\prime} = 0.78$

Along the curve

Lecture brief

Historical brief

d’Alembert’s wave equation, Snell, the thin-lens maker, Doppler and Bragg interference are the classical optics-and-sound toolkit. The lab is propagation, image and shift. This sheet (WAV-01 — Harmonic wave speed) is the form associated with d'Alembert 1747. Working symbols: $f$ , $\lambda$ $\rightarrow$ $v$ . d'Alembert's solution f(x±ct) travels at c. A harmonic wave of frequency f and wavelength λ has c = f λ.

Purpose

Purpose: compute

v

from

f

\lambda

in Waves & optics via

v=f\lambda=\omega/k

v = f λ = ω / k. Use it when a real waves & optics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

f = 440.000\,\mathrm{Hz}

\lambda = 0.780\,\mathrm{m}

, the governing relation

v=f\lambda=\omega/k

yields

v = 343.200\,\mathrm{m/s}

. Non-dispersive 1-D medium. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Frequency f440 HzWavelength \lambda0.78 m

Outputs

Phase speed v343.200 m/s

Reading speed

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Narration of this film

Non-dispersive 1-D medium.

d'Alembert's solution f(x±ct) travels at c. A harmonic wave of frequency f and wavelength λ has c = f λ.

Reading speed

Watch on YouTube