Question

The intensity level of sound in a truck is 92 dB. What is the intensity of this sound?

Answer 1

`~~1.58 xx10^-3 W/m^2`

Explanation:

`color(white)(-------)color(blue)[beta = 10log(I/I_o)`

Where
`I = "sound intensity level (x)"`
`I_o = "human threshold of hearing" (1xx10^-12 W/m^2)`
`beta = "sound intensity in dB (92 dB)"`

This is how the problem is setup

`color(white)(----)92 = 10log((x)/(1xx10^-12 W/m^2))`

Now, we just solve for our sound intensity level `(x)`

`color(white)(-------)`

Steps

• `92 = 10log((x)/(1xx10^-12 W/m^2))`

• `92/10 = cancel(10/10)log((x)/(1xx10^-12 W/m^2))`

• `9.2 = underbracelog((x)/(1xx10^-12 W/m^2))_(color(red)"rewrite using log rules")`

• `9.2 = log(x) - log(1xx10^-12 W/m^2)`

• `9.2 = log(x) - stackrel"-12"cancel[log(1xx10^-12 W/m^2)`

• `9.2 = log(x) +12`

• `-2.8 = log(x)`

• `10^-2.8 = x`

• `color(magenta)[1.58 xx 10^-3 W/m^2] ~~ color(magenta)[x`

`color(magenta)["Answer": 1.58 xx 10^-3 W/m^2] ~~ color(magenta)x`