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Need help understanding an equation in acoustics module

Posted 7 sept. 2021, 00:59 UTC−4 General, Acoustics & Vibrations, Equation-Based Modeling 1 Reply

Tithi Desai
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Hi all,

I am trying to understand the equation :

[https://doc.comsol.com/5.6/doc/com.comsol.help.aco/images/aco_ug_pressure.05.050.1.png]

Could someone please help me with this one ? Like just explain in simple terms ?

Thank you.

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Tithi
1 Reply Last Post 8 sept. 2021, 03:24 UTC−4
Acculution ApS Certified Consultant
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Posted: 3 years ago 8 sept. 2021, 03:24 UTC−4
Updated: 3 years ago 8 sept. 2021, 04:41 UTC−4

This is the acoustic wave equation; the governing equation for standard acoustics. https://en.wikipedia.org/wiki/Acoustic_wave_equation

It is comprised of several other equations regarding continuity and momentum.

If you remove the sources q and Q and assume that density is constant you have a simpler version, where it is even more clear to see how the second time derivative relates directly to the second spatial derivative. This so-called hyperbolic differential equation will give you waves as solutions; just try and plug in a cosine and differentiate twice with respect to time and twice with respect to space (you can assume 1D starting out, so d2p/dx2). You will see that the equation holds. So we expect the acoustic field obeying this original equation to be waves.

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René Christensen, PhD
Acculution ApS
www.acculution.com
info@acculution.com
This is the acoustic wave equation; the governing equation for standard acoustics. https://en.wikipedia.org/wiki/Acoustic_wave_equation It is comprised of several other equations regarding continuity and momentum. If you remove the sources q and Q and assume that density is constant you have a simpler version, where it is even more clear to see how the second time derivative relates directly to the second spatial derivative. This so-called hyperbolic differential equation will give you waves as solutions; just try and plug in a cosine and differentiate twice with respect to time and twice with respect to space (you can assume 1D starting out, so d2p/dx2). You will see that the equation holds. So we expect the acoustic field obeying this original equation to be waves.

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