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.
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