Urgent help- Q on Loudness/Intensity

**tashh01** · Oct 13th 2007, 01:22 AM

hello
I have this horrible question on loudness. It has given me the formula which is:

L=10Log(I/Io)

I also have a table as shown below.

Sound intensity (I) W/m2 Source of Sound

10-12.8 Inaudible to most humans

10-12.6

10-12.4

10-12.2

10-12 Threshold of Hearing

10-11.8

10-11.6
10-11.4 Very Quite Whisper

10-11.2

10-11 Rustle of Leaves

Now they want me to fill in a table which has I, Io and 10Log(I/Io).
I understand that "I" just means 10-11ect. But what is Io?? Now I know that Io is usually taken as 10-12 but that is only for like the softest sound or something..right??

Sorry its a little complicated to read cause of the table but please someone help!!! it will be much appreciated!!!

thanks,

natasha

**ticbol** · Oct 13th 2007, 02:44 AM

Reason why nobody is touching your question is nobody can understand it fully.

What is 11-12.8?
Is that 11 to 12.8?
I suspect that's what it means?

What is W/m2?
Is that Watts/ (m^2)?

The Log in the Log(I / Io)?
Is that Log to the base 10?

As you asked also, what is Io?
The initial I?
So in the "10-12.8", the Io is 10, and the I is 12.8?

If yes to all (the W/m2 not that important), then,
for the given 10-12.8,
Io = 10
I = 12.8
10Log(I /Io) = 10Log(12.8 /10) = 1.0721

Then just repeat that for the rest.

**topsquark** · Oct 13th 2007, 03:10 AM

Originally Posted by ticbol

What is W/m2?
Is that Watts/ (m^2)?

The Log in the Log(I / Io)?
Is that Log to the base 10?

As you asked also, what is Io?
The initial I?
So in the "10-12.8", the Io is 10, and the I is 12.8?

This information is standard for this kind of problem and may be assumed.

tashh01: You must remember that you are posting these questions on a Math forum, not Physics or Physical Science. Yes, there are people here to answer your question, but many of them have not taken your level of Physics as I and a few others have.

Feel free to go ahead and post your questions, but please remember to include a bit of background to your question. That way there will be a larger pool of members that can help you.

-Dan

**tashh01** · Oct 13th 2007, 04:52 AM

Ok iam going to try it again...

This is all the information I have:

L=10Log10(I/Io)

where: L= the loudness of sound measured in decibels (dB)
I= the sound intensity (in watts per square metre)
Io= the intensity of a reference sound. This is usually taken to be 10^-12 (in watts per square metre)

I also was given a table which has values for sound intensity (I) in watts/m^2 and source of sound. The information from the table is below:

Sound Intensity
10^-12.8, source of sound: inaudible to most humans
10^-12.6, source of sound: nothing is written here
10^-12.4, source of sound: nothing is written here
10^-12.2, source of sound: nothing is written here
10^-12, source of sound: Threshold of Hearing (Io)
10^-11.8, source of sound: nothing is written here
10^-11.6, source of sound: nothing is written here
10^-11.4, source of sound: very quite whisper
10^-11.2, source of sound: nothing is written here
10^-11, source of sound: rustle of leaves

Now from this information it wants me to complete a table with the headings I, I/Io and 10Log10(I/Io).

Iam thinking that "I" is just the values given in the table for Sound intensity

Then to work out I/Io, I need Io...which is I dont understand how to get...or really what it is...It is usually taken as 10^-12...but it cant be taken like that all the time especially for a sound that humans cannot hear.

hopefully my question makes more sense now.

tash

**topsquark** · Oct 13th 2007, 05:18 AM

Originally Posted by tashh01

Ok iam going to try it again...

This is all the information I have:

L=10Log10(I/Io)

where: L= the loudness of sound measured in decibels (dB)
I= the sound intensity (in watts per square metre)
Io= the intensity of a reference sound. This is usually taken to be 10^-12 (in watts per square metre)

I also was given a table which has values for sound intensity (I) in watts/m^2 and source of sound. The information from the table is below:

Sound Intensity
10^-12.8, source of sound: inaudible to most humans
10^-12.6, source of sound: nothing is written here
10^-12.4, source of sound: nothing is written here
10^-12.2, source of sound: nothing is written here
10^-12, source of sound: Threshold of Hearing (Io)
10^-11.8, source of sound: nothing is written here
10^-11.6, source of sound: nothing is written here
10^-11.4, source of sound: very quite whisper
10^-11.2, source of sound: nothing is written here
10^-11, source of sound: rustle of leaves

Now from this information it wants me to complete a table with the headings I, I/Io and 10Log10(I/Io).

Iam thinking that "I" is just the values given in the table for Sound intensity

Then to work out I/Io, I need Io...which is I dont understand how to get...or really what it is...It is usually taken as 10^-12...but it cant be taken like that all the time especially for a sound that humans cannot hear.

hopefully my question makes more sense now.

tash

$I_0$ is called a "threshold" intensity: it is the sound intensity such that a human can barely hear it. So any sound intensity less than this cannot be heard.

You are correct about your first heading: you were given the I values.

So the $\frac{I}{I_0}$ column will simply be
$\frac{I}{10^{-12}~W/m^2}$ .

Then the last column will be simply $10log\left ( \frac{I}{I_0} \right )$ .

Lots of calculating, but not too heavy on the Math, overall.

-Dan

**tashh01** · Oct 13th 2007, 05:31 AM

Originally Posted by topsquark

$I_0$ is called a "threshold" intensity: it is the sound intensity such that a human can barely hear it. So any sound intensity less than this cannot be heard.

You are correct about your first heading: you were given the I values.

So the $\frac{I}{I_0}$ column will simply be
$\frac{I}{10^{-12}~W/m^2}$ .

Then the last column will be simply $10log\left ( \frac{I}{I_0} \right )$ .

Lots of calculating, but not too heavy on the Math, overall.

-Dan

Ok..sorry but Iam still a little confused though because for example, 10^-12.8 is an intensity which as the table says is "inaudible to humans" so therefore Io cannot be 10^-12 W/m^2 at this point cause that would mean humans can hear the sound as it within the threshold of hearing. Right??? lol

Sorry again this probably is a really simple question that Iam just making hard...

**topsquark** · Oct 13th 2007, 05:35 AM

Originally Posted by tashh01

Ok..sorry but Iam still a little confused though because for example, 10^-12.8 is an intensity which as the table says is "inaudible to humans" so therefore Io cannot be 10^-12 W/m^2 at this point cause that would mean humans can hear the sound as it within the threshold of hearing. Right??? lol

Sorry again this probably is a really simple question that Iam just making hard...

No problem, just take things as they are:
$\frac{I}{I_0} = \frac{10^{-12.8}~W/m^2}{10^{-12}~W/m^2} = 10^{-0.8} \approx 0.158489$

So
$10log\left ( \frac{I}{I_0} \right ) = -8$

Just because a sound can't be heard doesn't mean it doesn't have a sound intensity.

-Dan

**tashh01** · Oct 13th 2007, 05:48 AM

Originally Posted by topsquark

No problem, just take things as they are:
$\frac{I}{I_0} = \frac{10^{-12.8}~W/m^2}{10^{-12}~W/m^2} = 10^{-0.8} \approx 0.158489$

So
$10log\left ( \frac{I}{I_0} \right ) = -8$

Just because a sound can't be heard doesn't mean it doesn't have a sound intensity.

-Dan

oh my god your right....it all makes sense!!!

so I'll just take all of the Io's as 10^-12. Wow...I feel really stuipd right now...it was so simple. lol
thanks so much for your help! Iam much less stressed now

tash

**topsquark** · Oct 13th 2007, 05:52 AM

Originally Posted by tashh01

oh my god your right....it all makes sense!!!

so I'll just take all of the Io's as 10^-12. Wow...I feel really stuipd right now...it was so simple. lol
thanks so much for your help! Iam much less stressed now

tash

You aren't stupid. Everyone has problems with one thing or another.

Glad to hear you are less stressed now.

-Dan

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