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Math Help - Urgent help- Q on Loudness/Intensity

  1. #1
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    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

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  2. #2
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    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.
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ticbol View Post
    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
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    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
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by tashh01 View Post
    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
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    Quote Originally Posted by topsquark View Post
    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...
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  7. #7
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by tashh01 View Post
    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
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    Quote Originally Posted by topsquark View Post
    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
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  9. #9
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by tashh01 View Post
    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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