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Hal Repasky

I don't really know if this is what you are looking for of if I am on
the right track here, but, you asked a question about sound intensity
and the relationship between the Relative Intensity level in decibels
and the Amplitude of the sound.  I didn't see anything wrong with
what you presented, but would have the following additional comments
(interspersed with your original):

>
>I know that Power is proportional to amplitude squared   P = k A*A
>

True.  A is the Amplitude of the vibrations of the air molecules, or the
amplitide of the pressure variations in the air produced by the sound.

>and that Intensity is proportional to Power    I = P/Area (crosssectional)
>

True, but, sound spreads in a spherical "front", so the area here
is:
                    4(pi)r*r       , the area of a sphere of radius, r.

>but (R.I.)  Relative Intensity = 10 Log (I/Io)  in dB's
>

True, and Io = 1x10exp(-12) Watts/meter squared.  The value of
Io is considered to be the threshold of human hearing, and
so this gives the Relative Intensity a value of 0 decibels (dB) at the lower
threshold and a value of about 120 dB at the threshold of pain for
humans (about 1 Watt/meter squared).

>Does that mean R.I. is proportional to the Log of A*A?
>

Not quite.  Remember, when you take logrithms that logs of products
are sums of the logs.  (ie, log(2x7) = log(2) + log(7)).  So, the R.I.
is 10 log(I/Io) = 10 log (P/AIo).  Substituting gives

R.I. = 10 log (kA*A/4(pi)r*r) = 10{log (k/4(pi)) + log (A*A/r*r)}.

        = 10 log(k/4(pi)) + 10 log(A*A/r*r)

So, there are really two variables, A the amplitude of the vibrations
set up in the air molecules by the sound source, and r, the radius (or
distance)between the sound source and receiver (ear?).

>What I am trying to find is the easy? or basic relationship between
>
>R.I. and Amplitude...
>
>Anyone out-there can you explain better!?
>
>Thanks,

I don't know if this helps or if it complicates things.  Good luck on the
project with your Physics class.

Hal Cox

(hcox@ec.sdcs.k12.ca.us)

Science Department
Hoover High School
4474 El Cajon Blvd.
San Diego, CA  92115

Voice: (619) 283-6281(ext274)