Question

The formula B=10log(i/i0) is used to find the sound level, , in decibels (dB), of a sound with an intensity of I. In the formula, represents the smallest sound intensity that can be heard by the human ear (approximately ).

What is the sound intensity of a noise that is 130 dB?

The sound intensity is
.

Answer 1

Answer:

The Answer is 10 watts/meter^2.

Step-by-step explanation:

Substitute 130 for B.

Substitute 10^-12 for i0.

I am not going to write absolutly everything because I would be here for days lol

Answer 2

The sound intensity is 10 watts/meter^2.

We have given that the formula

$B=10log(I/I_0)$

We have B=130

Substitute 130 for B.

$I_0$ is the intensity that can be heard by human ear and that is

$10^{-12} Watt/m^2$

Substitute 10^-12 for $I_o$

$130=10log(I/10^{-12} )\\10\log _{10}\left(\frac{I}{10^{-12}}\right)=130$

divide both side by 10

$\frac{10\log _{10}\left(\frac{I}{10^{-12}}\right)}{10}=\frac{130}{10}$

$\log _{10}\left(\frac{I}{10^{-12}}\right)=13$

Which log rule we use here?

$log_{e}a=C \implies a=e^{C}$

Therefore, we get

$\frac{I}{10^{-12}}=10^{13}$

$I\times10^{12}=10^{13}\\I=10$

Therefore the sound intensity is 10 watts/meter^2.

To learn more about the sound intensity visit:

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