Int. Word problem

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caligirl350

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Feb 8, 2010
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Use the formula L = 10 ? log 1/10, where the loudness of a sound in decibels is determined by I, the number of watts per square meter produced by the soundwave, and I0 = 10-^12 w/m2. A certain noise measures 30 dB. If the intensity is multiplied by 10, how many decibels will the new noise measure?

well, if I have to guess I would say 300. This problem is way out of my league. Thanks to some help on this board I have been able to manage my other problems. I am unable to tackle this one.
 
The logarithmic scale is not directly proportional. Multiplying one side by 10 does not result in the other side being multiplied by 10.

From Google reference:

First, remember that the decibel (dB) is a logarithmic unit,
meaning that you cannot add and subtract dB like ordinary numbers. For
example, an increase of 10 dB means that the
sound is 10 times as loud; i.e., 70 dB is 10 times as loud as 60 dB.

So, if some sound with an intensity of I measures 30 decibels (dB), then increasing I tenfold to 10*I increases the decibel measurement by adding 10 more dB. In other words, we multiply the logarithmic argument by 10 on the right, but we add 10 to the number of decibels on the left.

30 = 10 * log(I/I[sub:1hbjzopp]0[/sub:1hbjzopp])

30 + 10 = 10 * log(10*I/I[sub:1hbjzopp]0[/sub:1hbjzopp])

The answer is 40 dB.

We can show this, and also demonstrate that the value of I[sub:1hbjzopp]0[/sub:1hbjzopp] is not relevant, by using a system of two equations.

30 = 10*log(I/I[sub:1hbjzopp]0[/sub:1hbjzopp])

L = 10*log(10*I/I[sub:1hbjzopp]0[/sub:1hbjzopp])

Here, we see that intensity I results in a sound that measures 30 dB, and increasing the intensity to 10*I results in some new number of decibels L.

Solve each equation for I[sub:1hbjzopp]0[/sub:1hbjzopp], and equate the results. That eliminates the symbol I[sub:1hbjzopp]0[/sub:1hbjzopp], altogether.

Solving the resulting equation for L yields 40.
 
caligirl350 said:
I am still a little confused
Click to expand...

If you were to explain more about what's confusing, to you, I would probably be able to talk about those things in greater detail.

Are you able to solve the system of two equations for L?
 
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