Combining two different sound intensities

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The discussion focuses on calculating the combined sound intensity levels of two sounds, one fixed at 70 dB and the other varying from 50 to 90 dB. Participants clarify that the decibel levels cannot be directly added, as the formula requires actual intensities, not decibel values. The correct approach involves converting each dB level to intensity using the formula SIL = 10 log(I/I0) and then summing the intensities before converting back to dB for the total level. A general observation is made that when one sound is significantly stronger than the other, the combined level will be closer to the stronger sound's intensity. Understanding the relationship between intensity and decibels is crucial for accurate calculations.
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Consider a fixed sound of intensity level SIL1 = 70 dB and another (of different frequency) whose intensity level takes on the series of values SIL2 = 50, 60, 70, 80 and 90 dB.
(a) To the nearest dB, what is the level of the combined sound in each case?
(b) Make a general statement about the combined level for any two sounds when one is much stronger than the other.

Relevant equations
SIL=10log(I/Io)

I tried to do SIL=10log(70+50) for the first one, but I don't think that's right. Do you divide them instead?
 
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##70\text{dB} = 10\log(I_1/I_0)##
##50\text{dB} = 10\log(I_2/I_0)##
... and so on. Do you see where you are going wrong?
 
No, your equations don't seem to make sense to me...?
 
Definition of "decibels":

SIL=10log(I/Io) is what you wrote down. Make sure you understand this relation.

SIL is the decibel intensity level.
I is the actual sound intensity.
I0 is some reference intensity.
When you wrote SIL=10log(70+50) you put the decibel levels inside the log where actual intensities go.

Thus, SIL1=70dB implies a sound intensity of I so that 70dB=10log(I/I0).
 
okay yes that makes much more sense, but how do I solve it? Do i replace Io with the W/m^2 number? Ex for 70dB=10log(I1/Io) : Io-10^-12 and I=10^-5?
and then just add the two answers together to create the combined sound in each case?
 
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From the definition of SLI:##SLI_{tot}=10\log(I_{tot}/I_0)##
You need to know how to get the total intensity from the individual intensities.

What you have to do then, is derive the relation that gives you ##SLI_{tot}## in terms of ##SLI_1## and ##SLI_2##. I mean - in general. Just do the algebra first, then put the numbers in.

Does it matter if you don't know what ##I_0## is?
 
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