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

1. Dec 5, 2017

### Nunzio Luigi

Hello everyone! :-)

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

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?

Cheers,
Nunzio Luigi

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Last edited by a moderator: Dec 5, 2017
2. Dec 10, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

3. Dec 10, 2017

### Gordianus

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.