# Homework Help: Sound Intensity Level of Three Objects

1. Oct 21, 2012

### songoku

1. The problem statement, all variables and given/known data
Given that:
TI1 + TI2 = 70 dB
TI2 + TI3 = 80 dB

Find TI1 + TI2 + TI3

2. Relevant equations
TI = 10 log (I/Io)

3. The attempt at a solution
From that two equations, I got:
I1.I2 = 10-17
I2.I3 = 10-16
I1.I22.I3 = 10-33

Then stuck....

2. Oct 21, 2012

### Spinnor

"1. The problem statement, all variables and given/known data
Given that:
TI1 + TI2 = 70 dB
TI2 + TI3 = 80 dB

Find TI1 + TI2 + TI3"

Don't you have three unknowns and only two equations, your stuck?

3. Oct 22, 2012

### songoku

Sorry I don't really get what you mean. But anyway, how to solve for three unknowns with only two equations?

4. Oct 23, 2012

### Spinnor

I think I'm mistaken above. See page 5 of the following link for examples of adding sounds. If you are still having trouble I will give it a second shot.

http://faculty.delhi.edu/hultendc/AECT350-Lecture%202-REV.pdf [Broken]

Last edited by a moderator: May 6, 2017
5. Oct 23, 2012

### songoku

Let us discuss the question in the your link first, page 5.

The answer for example 1 is 100.41 dB. I tried other working and got different result. Here it is:
L1 = sound intensity level = 100 dB and L2 = 90 dB

L = 10 log (I/Io), where Io = 10-12

L1 = 100
10 log (I1/Io) = 100
log (I1/10-12) = 10
I1/10-12 = 1010
I1 = 10-2 W/m2

With the same working, I2 = 10-3 W/m2

Ltotal = L1 + L2
= 10 log (I1/Io) + 10 log (I2/Io)
= 10 I1 - 10 log 10-12 + 10 log I2 - 10 log 10-12
= 10 log (I1.I2) + 240
= 10 log 10-5 + 240
= 190 dB

Where is my mistake?

Last edited by a moderator: May 6, 2017
6. Oct 28, 2012

### ehild

The loudness is not additive. Add the powers, and calculate the resultant loudness from resultant power.

I=I1+I2= (0.01+0.001) W/m2
L=10 log(0.011/10-12))

ehild

7. Oct 28, 2012

### songoku

Oh ok. But how to solve my question? I don't think we can find the sound intensity or power

8. Oct 28, 2012

### ehild

I do not understand the original problem. What are Tl1, Tl2, Tl3? Is the original question the same what you wrote?

ehild

9. Oct 28, 2012

### songoku

Yes, that's all the problem given, verbatim.

TI there is sound intensity, exactly the same as L, expressed in dB and has formula:
TI = L = 10 log (I/Io), where Io = 1012

10. Oct 28, 2012

### ehild

Sorry, I still do not understand what was meant on the '+'. The loudness of two sounds is not the sum of the loudnesses. Was it said that the resultant loudness of two sounds is 70 db or the sum of loudnesses is 70 db? Anyway, there are three unknowns and two equation, you can not get numerical solution. Ask your teacher what he/she meant.

ehild

11. Oct 28, 2012

### songoku

Ok I will. Anyway, what is the difference between "the resultant loudness of two sounds is 70" and "the sum of loudnesses is 70 db"?

12. Oct 28, 2012

### ehild

You saw it in the previous problem, when the resultant of the 100 db and 90 db sources was the question. You added the intensities (power/unit area) and calculated the loudness (dB) from it, instead of adding the decibel values.
I wonder if your teacher meant that the loudness of the resultant intensity of two sound sources is 70 dB or really the sum of two dB values is 70 as you wrote in the original post.

ehild

13. Oct 29, 2012

### songoku

So can I say that "the sum of loudnesses is 70 db" does not exist and "the resultant loudness of two sounds is 70" is the correct term?

If the question asks about "the resultant loudness of the three sounds", can we solve it?

14. Oct 30, 2012

### ehild

No, with two equation for three unknows.

ehild

15. Oct 31, 2012

### songoku

OK thanks for the help