Can Initial Intensity Differ from Incident Intensity?

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SUMMARY

The discussion centers on the calculation of sound intensity levels using the formula Beta=10log(I/I0), where I0 is the reference intensity of 10-12 W/m2. It clarifies that while the reference intensity is typically used, one can also calculate the difference in sound levels between two intensities, Ia and Ib, by using the formula 10log(Ia/Ib). The example provided involves a speaker's power increase from 5 W to 50 W, leading to a sound level increase that can be calculated using the appropriate intensity values.

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  • Understanding of sound intensity and decibel levels
  • Familiarity with logarithmic functions
  • Knowledge of the reference intensity I0 = 10-12 W/m2
  • Basic principles of acoustics
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  • Learn how to apply the decibel formula in various sound intensity scenarios
  • Study the relationship between power and intensity in sound systems
  • Explore the concept of sound level differences using real-world examples
  • Investigate the effects of sound intensity on human perception
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Students studying acoustics, audio engineers, and anyone interested in understanding sound intensity calculations and their practical applications in sound systems.

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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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