Question

The level of sound (D), which is measured in decibels, is defined by the equation D=10log(I/10^-16), where I is the sound intensity measured in watts/cm². Determine the level in decibels of a sound that has an intensity I = 10^-6 watts/cm². I don't understand where to go after plugging in I.

Answer 1

Step 1

Define terms

The equation is

`D=10*\log _(10)((I)/(10^(-16)))`

D=level of sound(decibels)

I = sound intensity (watts/cm²)

Step 2

Substitute and find the value of D

`\begin{gathered} I=10^(-6)wattspercm^2 \\ D=10*\log _(10)((I)/(10^(-16))) \\ D=10*\log _(10)((10^(-6))/(10^(-16))) \\ D=\text{ 10}*\log _(10)(10^(-6-(-16))) \end{gathered}`
`\begin{gathered} D=\text{ 10}*\log _(10)(10^(10)) \\ D=10\text{ }*10 \\ D=\text{ 100 decibels} \end{gathered}`

Hence the level in decibel D of the sound = 100 decibels