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 dont think thats 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?