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WAV-29

Sound pressure level

SPL re 20 µPa.

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GoverningSound pressure level

Governing equation

Lp=20log⁡10(p/p0)L_p=20\log_{10}(p/p_0)

p∈[2×10−5,20]p \in \left[2\times 10^{-5}, 20\right]

where

p
p (Pa)
Lp
Sound pressure level (dB)

The figure, part by part

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WAV-29 · wave
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①

Governing law — red

Lp=20log⁡10(p/p0)L_p=20\log_{10}(p/p_0)

p∈[2×10−5,20]p \in \left[2\times 10^{-5}, 20\right]

p=2×10−5p = 2\times 10^{-5}Lp=0Lp = 0

②

Domain of the variable — blue

pmin⁡=2×10−5,pmax⁡=20p_{\min} = 2\times 10^{-5},\quad p_{\max} = 20

p∈[2×10−5,20]p \in \left[2\times 10^{-5}, 20\right]

p=2×10−5p = 2\times 10^{-5}p=2×10−5p = 2\times 10^{-5}

③

Response curve — green

Lp=20log⁡10(p/p0)L_p=20\log_{10}(p/p_0)

p∈[2×10−5,20]p \in \left[2\times 10^{-5}, 20\right]

p=2×10−5p = 2\times 10^{-5}Lp=0Lp = 0

④

Rate of change — amber

dLpdp\frac{\mathrm{d}Lp}{\mathrm{d}p}

p∈[2×10−5,20]p \in \left[2\times 10^{-5}, 20\right]

p=0.126p = 0.126Lp′=325.9Lp^{\prime} = 325.9

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-29 — Sound pressure level) is the form associated with Sound pressure level. Working symbols: pp →\rightarrow LpLp. SPL re 20 µPa. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute LpLp from pp in Waves & optics via Lp=20log⁡10(p/p0)L_p=20\log_{10}(p/p_0) SPL re 20 µPa. 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 p=0.200 Pap = 0.200\,\mathrm{Pa}, the governing relation Lp=20log⁡10(p/p0)L_p=20\log_{10}(p/p_0) yields Lp=80.000 dBLp = 80.000\,\mathrm{dB}. 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

Outputs

  • Sound pressure level Lp80.000 dB
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WAV-29 · wave
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Narration of this film

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

SPL re 20 µPa. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube