Combining two different sound intensities

1. Feb 19, 2013

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 dont think thats right. Do you divide them instead?

2. Feb 20, 2013

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?

3. Feb 20, 2013

ebmather

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

4. Feb 20, 2013

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).

5. Feb 20, 2013

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?

Last edited: Feb 20, 2013
6. Feb 20, 2013

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?