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bazaltina [42]
2 years ago
6

NO LINKS!!! Please help fill in the blanks. Part 10a.​

Mathematics
1 answer:
pogonyaev2 years ago
4 0

Sound level is measured in <u>  decibels  </u> (dB).

The equation \beta = 10\log\left(\frac{I}{I_0}\right), where I_0 is the intensity of the <u>   threshold  </u> sound a human can hear (10^{-12} \text{watts}/\text{meter}^2) and I is the <u>   intensity    </u> of the sound being measured, gives the sound level, \beta

Example:

What was the intensity of the launch of NASA's Saturn V rocket, about 200 dB?

\beta = 10\log\left(\frac{I}{I_0}\right)\\\\\text{Substitute.} \ 200 = 10\log\left(\frac{I}{10^{-12}}\right)\\\\\text{Isolate the log.} \ 20 = \log\left(\frac{I}{10^{-12}}\right)\\\\\text{Rewrite into exponential form.} \ \frac{I}{10^{-12}} = 10^{20}\\\\\text{Solve for the variable}\\ \ I = (10^{20})(10^{-12}) = 10^8 = 100,000,000 = \text{100 million watts/}m^2

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