SOLUTION: The decibel level of sound is given by: D= 10 log(I/10^-12) where I is the sound intensity measured in watts per square meter. Find the decibel level of a whisper at an intensity o

Algebra ->  Trigonometry-basics -> SOLUTION: The decibel level of sound is given by: D= 10 log(I/10^-12) where I is the sound intensity measured in watts per square meter. Find the decibel level of a whisper at an intensity o      Log On


   

Question 93361This question is from textbook Algebra and Trigonometry
: The decibel level of sound is given by: D= 10 log(I/10^-12) where I is the sound intensity measured in watts per square meter. Find the decibel level of a whisper at an intensity of 5.4x 10^-10 watts per square meter. This question is from textbook Algebra and Trigonometry

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given the formula for computing decibels of sound:
.
D=+10%2Alog%2810%2C%28I%2F%2810%5E-12%29%29%29
.
where I is the sound intensity measured in watts per square meter. The problem tells you
that a whisper with a sound intensity I of 5.4+%2A+10%5E%28-10%29 watts per square meter takes
place and asks you to find the decibel level. Begin by substituting 5.4+%2A+10%5E%28-10%29 for I
in the decibel equation. When you do that the equation becomes:
.
D=+10%2Alog%2810%2C%28%285.4%2A10%5E-10%29%2F%2810%5E-12%29%29%29
.
The rule for negative integers is that you can change them to a positive integer is the
quantity is moved from the denominator to the numerator or from the numerator to the denominator.
In this case move the 10%5E%28-12%29 from the denominator and change the exponent to +12.
This results in the equation becoming:
.
D=+10%2Alog%2810%2C%28%285.4%2A10%5E-10%29%2A%2810%5E12%29%29%29
.
Notice that you have two numbers each having an exponent. Since the two numbers are the same
(both are 10), you can just raise 10 to the sum of the exponents. The equation then is:
.
D=+10%2Alog%2810%2C%285.4%2A10%5E%28-10%2B12%29%29%29
.
which when you combine the exponents by adding them simplifies to:
.
D=+10%2Alog%2810%2C%285.4%2A10%5E2%29%29
.
but 10%5E%282%29+=+10%2A10+=+100
.
And replacing 10%5E2 by 100 results in
.
D=+10%2Alog%2810%2C%285.4%2A100%29%29
.
and 100 times 5.4 equals 540. This translates the problem to:
.
D=+10%2Alog%2810%2C%28540%29%29%29
.
Now using a scientific calculator you can find that log%2810%2C540%29+=+2.73239376 so
you can replace the entire log expression by 2.73239376 to get:
.
D+=10%2A2.73239376
.
and multiplying out the right side gives you the answer:
.
D+=+27.3239376 decibels.
.
Hope this helps you to understand the problem and also helps you to become familiar with
working with logarithms.
.