Question

Algebra 2 help?

5. A construction explosion has an intensity I of 1.25 x 10–4 W/m2. Find the loudness of the sound in decibels if W/m2. Round to the nearest tenth. (1 point)

81 decibels
161 decibels
82.2 decibels
12.5 decibels

The example question in the textbook is totally different so I'm not sure how to do this. I tried to make the equation and then got confused. An explanation would be great! Thanks

Answer 1

Decibels use a logarithmic scale. \[
dB = 10 \log_{10} \left[ \frac{I}{I_0} \right]
\]In this case, \(I_0\) is the threshold of hearing at \(10^{-12} W/m^2\).
Where as \(I\) is just going to be the intensity they gave you: \(1.25\times 10^{-4}W/m^2\).

source: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/intens.html

Answer 2

To understand what is going on... consider \[
\frac{I}{I_0} = c
\]This means: \[
I = c I_0
\]Basically, \(I\) is \(c\) times the intensity of the threshold of hearing. You want to find the \(c\), then you are the logarithm to make it so that \(c\) doesn't end up being so huge.

We use decibels because you end up having the intensity be something like 1000000 times the threshold, and big numbers like that make it hard for people to really understand. We can't comprehend them that well.

We do the same thing with measuring earth quake magnitudes too.

Answer 3

I think when I copy and pasted the question it left out some equations.

Find the loudness of the sound in decibels if \[L =10\log_{}\frac{ I }{ I 0} and I0=10^-12\] W/m2.

Answer 4

So I plugged in the values for 1.25 x 10^-4 / 10^-12 on a graphing calculator and got

1.25E-4 / 1E-12
= 125000000

Then I did the log to find L
10log I/I0
=10log 125000000
=80.96910013

So I guess the answer is 81 decibles.

Is this right?

Answer 5

It was right.