WAV-26

Acoustic Doppler

1-D source/observer Doppler.

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GoverningAcoustic Doppler

Governing equation

f'=f(v\pm v_o)/(v\pm v_s)

$vo \in \left[-40, 40\right]$

where

f: f (Hz)
v: v (m/s)
vo: vo (m/s)
vs: vs (m/s)
fp: Acoustic Doppler (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'=f(v\pm v_o)/(v\pm v_s)

$vo \in \left[-40, 40\right]$

$vo = -40$ $fp = 388.7$

Along the curve

②

Domain of the variable — blue

vo_{\min} = -40,\quad vo_{\max} = 40

$vo \in \left[-40, 40\right]$

$vo = -40$ $vo = -40$

Along the curve

③

Response curve — green

f'=f(v\pm v_o)/(v\pm v_s)

$vo \in \left[-40, 40\right]$

$vo = -40$ $fp = 388.7$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}fp}{\mathrm{d}vo}

$vo \in \left[-40, 40\right]$

$vo = -39.5$ $fp^{\prime} = 1.283$

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-26 — Acoustic Doppler) is the form associated with Acoustic Doppler. Working symbols: $f$ , $v$ , $vo$ , $vs$ $\rightarrow$ $fp$ . 1-D source/observer Doppler. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

fp

from

f

v

vo

vs

in Waves & optics via

f'=f(v\pm v_o)/(v\pm v_s)

1-D source/observer Doppler. 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}

v = 343.000\,\mathrm{m/s}

vo = 10.000\,\mathrm{m/s}

vs = 0.000\,\mathrm{m/s}

, the governing relation

f'=f(v\pm v_o)/(v\pm v_s)

yields

fp = 452.828\,\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

f f440 Hzv v343 m/svo vo10 m/svs vs0 m/s

Outputs

Acoustic Doppler fp452.828 Hz

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Narration of this film

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

1-D source/observer Doppler. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube