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#