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

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Answer 1 · 2017-06-05T03:16:52

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

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

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

$92 = 10log((x)/(1xx10^-12 W/m^2))$
$92/10 = cancel(10/10)log((x)/(1xx10^-12 W/m^2))$
$9.2 = underbracelog((x)/(1xx10^-12 W/m^2))_(color(red)"rewrite using log rules")$
$9.2 = log(x) - log(1xx10^-12 W/m^2)$
$9.2 = log(x) - stackrel"-12"cancel[log(1xx10^-12 W/m^2)$
$9.2 = log(x) +12$
$-2.8 = log(x)$
$10^-2.8 = x$
$color(magenta)[1.58 xx 10^-3 W/m^2] ~~ color(magenta)[x$

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