Combining two different sound intensities

[ebmather]

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?

 

[Simon Bridge]

$70\text{dB} = 10\log(I_1/I_0)$
$50\text{dB} = 10\log(I_2/I_0)$
... and so on. Do you see where you are going wrong?

 

[ebmather]

No, your equations don't seem to make sense to me...?

 

[Simon Bridge]

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).

 

[ebmather]

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?

 

[Simon Bridge]

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?