Sound Intensity Level of Three Objects

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Homework Help Overview

The discussion revolves around sound intensity levels of three objects, represented by equations relating their combined intensity levels in decibels (dB). The original poster presents two equations: TI1 + TI2 = 70 dB and TI2 + TI3 = 80 dB, and seeks to find the total intensity level of all three objects combined.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the implications of having three unknowns with only two equations, questioning the feasibility of finding a unique solution. Some express confusion about the meaning of the equations and the nature of the '+' operation in the context of sound intensity.

Discussion Status

There is an ongoing exploration of the definitions and assumptions underlying the problem. Some participants suggest that the loudness of sounds is not additive in a straightforward manner, prompting further inquiry into the original question's intent. Guidance has been offered regarding the interpretation of sound intensity and the need for clarity in the problem statement.

Contextual Notes

Participants note the potential ambiguity in the terms used, particularly regarding whether the equations represent resultant loudness or the sum of individual loudnesses. There is a consensus that the problem as stated may not allow for a numerical solution due to the lack of sufficient equations.

songoku
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Homework Statement


Given that:
TI1 + TI2 = 70 dB
TI2 + TI3 = 80 dB

Find TI1 + TI2 + TI3

Homework Equations


TI = 10 log (I/Io)

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...
 
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"1. Homework Statement
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?
 
Spinnor said:
"1. Homework Statement
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?

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

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
 
Last edited by a moderator:
Spinnor said:
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

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

The question is asking about Ltotal = L1 + L2, so:
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:
songoku said:
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

The question is asking about Ltotal = L1 + L2,

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
 
ehild said:
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

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

songoku said:

Homework Statement


Given that:
TI1 + TI2 = 70 dB
TI2 + TI3 = 80 dB

Find TI1 + TI2 + TI3
 
I do not understand the original problem. What are Tl1, Tl2, Tl3? Is the original question the same what you wrote?

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

ehild

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
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
ehild said:
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

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
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
ehild said:
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

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
songoku said:
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?

No, with two equation for three unknows.

ehild
 
  • #15
ehild said:
No, with two equation for three unknows.

ehild

OK thanks for the help :smile:
 

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