Question

A sound's noise level is measured in decibels (dB) by comparing the sound's intensity, $I$, to a benchmark sound that has an intensity of $10^{-16}$ watts/cm$^2$. In particular, $\text{dB} = 10 \log(I/10^{-16}) = 10 \log(10^{16}I)$. Note: Be sure to type $\log(x)$ for $\log$ base 10 of the variable $x$. A single jet engine that is 100 feet away from the listener has a noise level of 140dB. a) Find the sound intensity of the jet engine in watts/cm$^2$ $10^{-2}$ watts/cm$^2$ b) Suppose two jet engines are 100 feet away from a person, each with the same sound intensity as the jet engine from part (a). What is the combined noise level in decibels? [Hint: the combined sound intensity is the sum of the intensities of the two engines.] 143.0103 dB c) Suppose a source has sound intensity $I$. Using the definition of decibels, write an expression for the noise level in decibels if two sources with sound intensity $I$ are present. $D(I) = $ d) Using properties of logarithms, write the expression from part (c) as the sum of two logarithms. $D(I) = $

          A sound's noise level is measured in decibels (dB) by comparing the sound's intensity, $I$, to a benchmark sound that has an intensity of $10^{-16}$ watts/cm$^2$. In particular,
$\text{dB} = 10 \log(I/10^{-16}) = 10 \log(10^{16}I)$.
Note: Be sure to type $\log(x)$ for $\log$ base 10 of the variable $x$.
A single jet engine that is 100 feet away from the listener has a noise level of 140dB.
a) Find the sound intensity of the jet engine in watts/cm$^2$
$10^{-2}$ watts/cm$^2$
b) Suppose two jet engines are 100 feet away from a person, each with the same sound intensity as the jet engine from part (a). What is the
combined noise level in decibels? [Hint: the combined sound intensity is the sum of the intensities of the two engines.]
143.0103 dB
c) Suppose a source has sound intensity $I$. Using the definition of decibels, write an expression for the noise level in decibels if two sources with
sound intensity $I$ are present.
$D(I) = 
$
d) Using properties of logarithms, write the expression from part (c) as the sum of two logarithms.
$D(I) = $

A sound's noise level is measured in decibels (dB) by comparing the sound's intensity, I, to a benchmark sound that has an intensity of 10^-16 watts/cm^2. In particular,
dB = 10 log(I/10^-16) = 10 log(10^16I).
Note: Be sure to type log(x) for log base 10 of the variable x.
A single jet engine that is 100 feet away from the listener has a noise level of 140dB.
a) Find the sound intensity of the jet engine in watts/cm^2
10^-2 watts/cm^2
b) Suppose two jet engines are 100 feet away from a person, each with the same sound intensity as the jet engine from part (a). What is the
combined noise level in decibels? [Hint: the combined sound intensity is the sum of the intensities of the two engines.]
143.0103 dB
c) Suppose a source has sound intensity I. Using the definition of decibels, write an expression for the noise level in decibels if two sources with
sound intensity I are present.
D(I) =
d) Using properties of logarithms, write the expression from part (c) as the sum of two logarithms.
D(I) =

Added by Milagros M.

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