Sound Intensity Level of Three Objects

[songoku]

Homework Statement

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

Find TI₁ + TI₂ + TI₃

Homework Equations

TI = 10 log (I/I_o)

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...

 

[Spinnor]

"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?

 

[songoku]

"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?

 

[Spinnor]

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

 

[songoku]

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/I_o), where I_o = 10^-12

L₁ = 100
10 log (I₁/I_o) = 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 L_total = L₁ + L₂, so:
L_total = L₁ + L₂
= 10 log (I₁/I_o) + 10 log (I₂/I_o)
= 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?

 

[ehild]

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/I_o), where I_o = 10^-12

L₁ = 100
10 log (I₁/I_o) = 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 L_total = 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

 

[songoku]

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

Homework Statement

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

Find TI₁ + TI₂ + TI₃

 

[ehild]

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

ehild

 

[songoku]

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/I_o), where I_o = 10¹²

 

[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

 

[songoku]

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"?

 

[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

 

[songoku]

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?

 

[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?

No, with two equation for three unknows.

ehild

 

[songoku]

No, with two equation for three unknows.

ehild

OK thanks for the help