SOLUTION: The decible 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 decible level of a whisper at an intensity of

Question 72681: The decible 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 decible level of a whisper at an intensity of 5.4 ? 10-10 watts per meter.
Does anyone understand this? If so please break it down for me. Thanks to anyone who can help.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Since nobody else has taken a shot at this, I'll give it a go ...
.

.
is the equation that governs the relationship between sound intensity and decibels.
.
I think what you meant for the given sound intensity was
.
The units of your given intensity and the units of the intensity in the decibel equation
are consistent, so we can just substitute for I in the decibel
equation without having to make any conversion in units. With this substitution the decibel
equation becomes:
.

.
We can now divide the of the denominator into the of the
denominator. Recall that when you divide, you subtract exponents. The subtraction
of the exponents involves and this reduces to . Therefore,
the decibel equation becomes:
.

.
The rules of logarithms say that if you have the log of a product, you can split this into
the sum of the logs of each of the terms in the product. Applying this rule gives us:
.

.
The rule of exponents for logarithms says that an exponent comes out as the multiplier
of the log. So becomes . But is simply 1,
and therefore, reduces just to . Substitute this back into the
decibel equation and you get:
.

.
Finding the is just a calculator problem. It is or just round it
to which is probably close enough for your needs.
.
Substituting this value makes the equation:
.

.
So the answer appears to be 27.32 dB
.
Hope you could follow this through and that it helps you to understand this power ratio
equation.
RELATED QUESTIONS
The decibel level of sound by D=10 log(I/10^-12), where I is the sound intensity measured (answered by Nate)

I WOULD REALLY APPRECIATE IF IT SOMEONE HELPED ME WITH THIS PROBLEM: The decibel level... (answered by stanbon)

The decibel level of sound is given by D=10*log(I/10^-12), where I is the sound intensity (answered by Nate)

THE DECIBEL LEVEL OF SOUND IS GIVEN BY D=10 LOG(I/10^-12), WHERE I IS THE SOUND INTENSITY (answered by ankor@dixie-net.com)

The decibel level of sound is given by: D= 10 log(I/10^-12) where I is the sound... (answered by bucky)

A. The decibel level of sound is given by D=10log(I÷10^-12) where I is the sound... (answered by Boreal)

This looks quite not like anything I'm use to seeing and can't come up with the answer.... (answered by stanbon)

The decibel level of sound is given by D=10log(I/10^-12), where I is the sound intensity... (answered by ankor@dixie-net.com)

Hi, the decibel level of sound is given by D=10log(I/10^-12), where I is the sound... (answered by Nate)