# Urgent help- Q on Loudness/Intensity

• Oct 13th 2007, 01:22 AM
tashh01
Urgent help- Q on Loudness/Intensity
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:)

• Oct 13th 2007, 02:44 AM
ticbol
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)?

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.
• Oct 13th 2007, 03:10 AM
topsquark
Quote:

Originally Posted by ticbol
What is W/m2?
Is that Watts/ (m^2)?

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
• Oct 13th 2007, 04:52 AM
tashh01
Trying it again...
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
• Oct 13th 2007, 05:18 AM
topsquark
Quote:

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.

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
• Oct 13th 2007, 05:31 AM
tashh01
Quote:

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.

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...
• Oct 13th 2007, 05:35 AM
topsquark
Quote:

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
• Oct 13th 2007, 05:48 AM
tashh01
Quote:

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 :D

tash
• Oct 13th 2007, 05:52 AM
topsquark
Quote:

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 :D

tash

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

Glad to hear you are less stressed now. (Party)

-Dan