WAV-27

Beat frequency

Two close tones.

Reading speed

GoverningBeat frequency

Governing equation

f_b=|f_1-f_2|

$f2 \in \left[100, 800\right]$

where

f1: f1 (Hz)
f2: f2 (Hz)
fb: Beat frequency (Hz)

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

f_b=|f_1-f_2|

$f2 \in \left[100, 800\right]$

$f2 = 100$ $fb = 340$

Along the curve

②

Domain of the variable — blue

f2_{\min} = 100,\quad f2_{\max} = 800

$f2 \in \left[100, 800\right]$

$f2 = 100$ $f2 = 100$

Along the curve

③

Response curve — green

f_b=|f_1-f_2|

$f2 \in \left[100, 800\right]$

$f2 = 100$ $fb = 340$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}fb}{\mathrm{d}f2}

$f2 \in \left[100, 800\right]$

$f2 = 104.4$ $fb^{\prime} = -1$

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-27 — Beat frequency) is the form associated with Beat frequency. Working symbols: $f1$ , $f2$ $\rightarrow$ $fb$ . Two close tones. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

fb

from

f1

f2

in Waves & optics via

f_b=|f_1-f_2|

Two close tones. 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

f1 = 440.000\,\mathrm{Hz}

f2 = 445.000\,\mathrm{Hz}

, the governing relation

f_b=|f_1-f_2|

yields

fb = 5.000\,\mathrm{Hz}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

f1 f1440 Hzf2 f2445 Hz

Outputs

Beat frequency fb5.000 Hz

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Two close tones. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube