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Need help understanding an equation in acoustics module
Posted 7 set 2021, 00:59 GMT-4 General, Acoustics & Vibrations, Equation-Based Modeling 1 Reply
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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.
-------------------Tithi
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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.
-------------------René Christensen, PhD
Acculution ApS
www.acculution.com
info@acculution.com