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# What is the answer for question 18) ? http://postimg.org/image/6g52noj6f/

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What is the answer for question 18) ?

http://postimg.org/image/6g52noj6f/

Posted by lkballer24 on May 28, 2013 at 11:37 PM via web and tagged with math

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The sensation of loudness is approximately logarithmic to human ear. The unit used to express the acoustic intensity or power, therefore, is logarithmic. Decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities.

Thus, the ratio of a power value `I_1` to another power value `I_0` is represented by `L_(dB)` , that ratio expressed in decibels,which is calculated using the formula:

`L_(dB) = 10 log (I_1/I_0)`

The faintest audible sound having acoustic intensity of `1.0 *10^(-12) ` W/m^2 is the reference, `I_0` .

So, for the sound which is assigned 60 dB has actual acoustic intensity I, then

`60 = 10 log(I_1/(1.0 *10^(-12)))`

`=>`` log (I_1/(1.0 *10^(-12))) = 6`

`rArr` ` ``I_1/(1.0*10^-12)=10^6`

`rArr`  `I_1= 10^6*(1.0 *10^(-12))`

= `1.0 *10^(-6)` W/m^2

Now, for the sound assigned 120 dB has actual acoustic intensity `I_2` , then

`120 = 10 log(I_2/(1.0 *10^(-12)))`

`rArr`  `log (I_2/(1.0 *10^(-12))) = 12`

`rArr`  `I_2/(1.0*10^-12)=10^12`

`rArr`

`I_2 = 10^12*(1.0 *10^(-12)) `

`= 1.0` W/m^2

So, `I_2/I_1 = 10^6`

Therefore a 120 dB sound, usually associated with rock concerts, is actually one million times more powerful than a 60 dB sound of a conversation.

This could damage human audible system in a matter of minutes! This is how Jacob would probably be able to convince Anderson to take the ear protection plugs in the concert.

Posted by llltkl on May 29, 2013 at 1:21 AM (Answer #1)

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