About acoustics physics -- The Wave Equation and diminishing sound intensity

  • #1
Hello everyone! :-)
Actually I'm starting to understand acoustics physics and I figured actually out about this equation:

$$\frac{\partial^2\psi}{\partial t^2}=c^2 \nabla^2 \psi$$

which describes practically about pressure and propagation speed into space and time. I know also this equation describes practically also the decrement of sound intensity in time from a source to a destination...if we would talk about particle pressure it's decrement of pressure in space by inverse square-law.
So knowing, for spherical waves , the sound intensity in a certain point of time is:

$$I = \frac{W}{4\pi r^2}$$

and supposing to have a sound diffusor with max power output of 150W and knowing human ear voice range audibility is about 40dB-60dB and supposing I want to have I = 50dB at the time entering in my ear so how I can calculate which power output I have to set the sound diffusor to obtain that intensity I I said before?

Could you help me with this little example so I can understand and study all steps to obtain all values in all situations?

Thanks in advance to all!
Cheers,
Nunzio Luigi

<Moderator's note: LaTeX fixed. Please see https://www.physicsforums.com/help/latexhelp/>
 
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Answers and Replies

  • #2
286
35
The rms acoustic pressure at 94 dB SPL is 1 Pa. The acoustic intensity (far from the emitter) depends on the acoustic pressure as:##\it I=\frac{p^2}{\rho c}##, where ##\it\rho## is the density and ##\it c## the speed of sound. Now you can find different relationships between acoustic power, intensity, distance and SPL.
 

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