the loudness level of a sound can be expressed by comparing the sounds intensity to the intensity of a sound…

the loudness level of a sound can be expressed by comparing the sounds intensity to the intensity of a sound barely audible to the human ear. the formula d = 10(log i - log i_0) describes the loudness level of a sound, d, in decibels, where i is the intensity of the sound, in watts per meter², and i_0 is the intensity of a sound barely audible to the human ear. use this information to answer parts (a) and (b) below.\na. express the formula so that the expression in parentheses is written as a single - logarithm.\nd = □ (use parentheses to clearly denote the argument of each function.)

the loudness level of a sound can be expressed by comparing the sounds intensity to the intensity of a sound barely audible to the human ear. the formula d = 10(log i - log i_0) describes the loudness level of a sound, d, in decibels, where i is the intensity of the sound, in watts per meter², and i_0 is the intensity of a sound barely audible to the human ear. use this information to answer parts (a) and (b) below.\na. express the formula so that the expression in parentheses is written as a single - logarithm.\nd = □ (use parentheses to clearly denote the argument of each function.)

Answer

Explanation:

Step1: Apply log - subtraction rule

Recall the logarithm property $\log a-\log b = \log\frac{a}{b}$. Here $a = I$ and $b = I_0$. So $\log I-\log I_0=\log\frac{I}{I_0}$.

Step2: Substitute into original formula

Substitute $\log I - \log I_0=\log\frac{I}{I_0}$ into $D = 10(\log I-\log I_0)$. We get $D = 10\log\left(\frac{I}{I_0}\right)$.

Answer:

$D = 10\log\left(\frac{I}{I_0}\right)$