Answer:
hope it helps you (:
Step-by-step explanation:
Answer:
The decibel level of this second sound is 48.021 decibels.
Step-by-step explanation:
The acoustic intensity (
), measured in decibels, is defined by the following formula:
(1)
Where:
- Reference sound intensity, measured in watts per square meter.
- Real sound intensity, measured in watts per square meter.
If we know that
and
, then the real sound intensity of the first sound is:
![\frac{B_{dB}}{10} = \log_{10}\left(\frac{I}{I_{o}} \right)](https://tex.z-dn.net/?f=%5Cfrac%7BB_%7BdB%7D%7D%7B10%7D%20%3D%20%5Clog_%7B10%7D%5Cleft%28%5Cfrac%7BI%7D%7BI_%7Bo%7D%7D%20%5Cright%29)
![\frac{I}{I_{o}} = 10^{\frac{B_{dB}}{10} }](https://tex.z-dn.net/?f=%5Cfrac%7BI%7D%7BI_%7Bo%7D%7D%20%3D%2010%5E%7B%5Cfrac%7BB_%7BdB%7D%7D%7B10%7D%20%7D)
![I = I_{o}\cdot 10^{\frac{B_{dB}}{10} }](https://tex.z-dn.net/?f=I%20%3D%20I_%7Bo%7D%5Ccdot%2010%5E%7B%5Cfrac%7BB_%7BdB%7D%7D%7B10%7D%20%7D)
![I = \left(10^{-12}\,\frac{W}{m^{2}} \right)\cdot 10^{\frac{42\,dB}{10} }](https://tex.z-dn.net/?f=I%20%3D%20%5Cleft%2810%5E%7B-12%7D%5C%2C%5Cfrac%7BW%7D%7Bm%5E%7B2%7D%7D%20%5Cright%29%5Ccdot%2010%5E%7B%5Cfrac%7B42%5C%2CdB%7D%7B10%7D%20%7D)
![I = 1.585\times 10^{-8}\,\frac{W}{m^{2}}](https://tex.z-dn.net/?f=I%20%3D%201.585%5Ctimes%2010%5E%7B-8%7D%5C%2C%5Cfrac%7BW%7D%7Bm%5E%7B2%7D%7D)
The real sound intensity of the second sound is four times greater, that is:
If we know that
and
, then the acoustic intensity of the second sound is:
![B_{dB} = 10\cdot \log_{10}\left(\frac{I'}{I_{o}} \right)](https://tex.z-dn.net/?f=B_%7BdB%7D%20%3D%2010%5Ccdot%20%5Clog_%7B10%7D%5Cleft%28%5Cfrac%7BI%27%7D%7BI_%7Bo%7D%7D%20%5Cright%29)
![B_{dB} = 10\cdot \log_{10}\left(\frac{6.340\times 10^{-8}\,\frac{W}{m^{2}} }{10^{-12}\,\frac{W}{m^{2}} } \right)](https://tex.z-dn.net/?f=B_%7BdB%7D%20%3D%2010%5Ccdot%20%5Clog_%7B10%7D%5Cleft%28%5Cfrac%7B6.340%5Ctimes%2010%5E%7B-8%7D%5C%2C%5Cfrac%7BW%7D%7Bm%5E%7B2%7D%7D%20%7D%7B10%5E%7B-12%7D%5C%2C%5Cfrac%7BW%7D%7Bm%5E%7B2%7D%7D%20%7D%20%5Cright%29)
![B_{dB} = 48.021\,dB](https://tex.z-dn.net/?f=B_%7BdB%7D%20%3D%2048.021%5C%2CdB)
The decibel level of this second sound is 48.021 decibels.
It shows ratios of one thing in comparison to another. In this picture it shows favorite pizza toppings. You can easily see ore people like sausage versus any other topping. :)