Can Initial Intensity Differ from Incident Intensity?

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AI Thread Summary
The discussion centers on the use of initial intensity in the context of sound level calculations. It questions whether the initial intensity can be the previous intensity level rather than the standard reference intensity of 10^-12 W/m². The mathematical derivation shows that when comparing two intensities, the initial intensity can indeed be the previous level, allowing for calculations based on the ratio of the two intensities. An example problem is presented, where a speaker's power increase from 5 W to 50 W raises the sound level, prompting confusion about the correct values to use in calculations. Clarification is sought on the appropriate application of initial and incident intensities in these scenarios.
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Homework Statement



In the equation Beta=10log (I/I (initial)

is the I inital always the incident intensity 10^-12? Or if you are moving from one intensity to another, then can the initial intensity be the one you were initially at? For example, if you were moving from an intensity of 5 to 10, then could the initial be 5 instead of the incident intensity? If so, why?

Homework Equations



Given above.


The Attempt at a Solution



Well, I actually solved a problem in which something went from an initial intensity to a final, and plugged in the initial intensity and got the right answer, but I am confused on why you don't always use incident intensity?
 
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In principle you should always use the reference intensity of I0 = 10^(-12).
However, suppose you want to calculate the difference in sound level when going from intensity Ia to Ib. Then mathematics tells you that

10log( Ia / I0 ) - 10log( Ib / I0 ) = 10log( (Ia / I0) / (Ib / I0) ) = 10log( Ia / Ib )
 
CompuChip said:
In principle you should always use the reference intensity of I0 = 10^(-12).
However, suppose you want to calculate the difference in sound level when going from intensity Ia to Ib. Then mathematics tells you that

10log( Ia / I0 ) - 10log( Ib / I0 ) = 10log( (Ia / I0) / (Ib / I0) ) = 10log( Ia / Ib )

Well, could you help me work through this problem...

A speaker is producing a total of 5 W of sound, and you hear 10 dB. Someone turns up the
power to 50 W. What level of sound do you hear?
(a) 10 dB, (b) 15 dB, (c) 100 dB, (d) 40 dB, (e) 20 dB

I don't know why I plugged in 50/5 for I and I initial after I used the math function you gave. Please help.
 

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