Why Do We Use the Complex Conjugate of Velocity to Calculate Acoustic Intensity?

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SUMMARY

The discussion centers on the necessity of using the complex conjugate of velocity when calculating complex acoustic intensity. Specifically, the multiplication of the complex conjugate of velocity with complex pressure is analogous to the calculation of apparent electrical power, where the correct phase angle is critical. This method ensures that the phase relationship between the velocity and pressure is accurately represented, preventing erroneous phase calculations that would arise from using the velocity alone.

PREREQUISITES
  • Understanding of complex numbers and their conjugates
  • Familiarity with acoustic intensity concepts
  • Knowledge of phasor representation in electrical engineering
  • Basic principles of wave mechanics
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  • Study the derivation of complex acoustic intensity formulas
  • Learn about phasor analysis in electrical circuits
  • Explore the relationship between pressure and velocity in acoustics
  • Investigate the implications of phase angles in wave interactions
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Acoustics engineers, electrical engineers, and physics students interested in wave mechanics and the mathematical representation of acoustic phenomena.

Radel
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Hello All,

I would like to know why do we multiply the complex conjugate of velocity (not just the velocity) with the complex pressure to obtain the complex acoustic intensity. Could someone please help me with this?

Regards,
Radel...
 
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I guess for the same reason the apparent electrical power in complex form is given by S = VI*. Correct phase angle between voltage phasor V=V⋅ev and current phasor I=I⋅ei is φ=φvi. Without conjugate you would get in the product φ=φvi. Conjugate of the current I*=Ie-jφi solves this problem since S=VI*=V⋅ev⋅I⋅e-jφi=V⋅I⋅ej(φvi).
 

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