All fluids exert pressure like the air inside a tire. The particles of fluids are constantly moving in all directions at random. As the particles move, they keep bumping into each other and into anything else in their path. These collisions cause pressure, and the pressure is exerted equally in all directions.
is the intensity of the sound.
Answer: Option B
<u>Explanation:</u>
The range of sound intensity that people can recognize is so large (including 13 magnitude levels). The intensity of the weakest audible noise is called the hearing threshold. (intensity about
). Because it is difficult to imagine numbers in such a large range, it is advisable to use a scale from 0 to 100.
This is the goal of the decibel scale (dB). Because logarithm has the property of recording a large number and returning a small number, the dB scale is based on a logarithmic scale. The scale is defined so that the hearing threshold has intensity level of sound as 0.
![\text { Intensity }(d B)=(10 d B) \times \log _{10}\left(\frac{I}{I_{0}}\right)](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Intensity%20%7D%28d%20B%29%3D%2810%20d%20B%29%20%5Ctimes%20%5Clog%20_%7B10%7D%5Cleft%28%5Cfrac%7BI%7D%7BI_%7B0%7D%7D%5Cright%29)
Where,
I = Intensity of the sound produced
= Standard Intensity of sound of 60 decibels = ![1 \times 10^{-12} \mathrm{Wm}^{-2}](https://tex.z-dn.net/?f=1%20%5Ctimes%2010%5E%7B-12%7D%20%5Cmathrm%7BWm%7D%5E%7B-2%7D)
So for 19 decibels, determine I as follows,
![19 d B=(10 d B) \times \log _{10}\left(\frac{I}{1 \times 10^{-12} W m^{-2}}\right)](https://tex.z-dn.net/?f=19%20d%20B%3D%2810%20d%20B%29%20%5Ctimes%20%5Clog%20_%7B10%7D%5Cleft%28%5Cfrac%7BI%7D%7B1%20%5Ctimes%2010%5E%7B-12%7D%20W%20m%5E%7B-2%7D%7D%5Cright%29)
![\log _{10}\left(\frac{1}{1 \times 10^{-12} \mathrm{Wm}^{-2}}\right)=\frac{19}{10}](https://tex.z-dn.net/?f=%5Clog%20_%7B10%7D%5Cleft%28%5Cfrac%7B1%7D%7B1%20%5Ctimes%2010%5E%7B-12%7D%20%5Cmathrm%7BWm%7D%5E%7B-2%7D%7D%5Cright%29%3D%5Cfrac%7B19%7D%7B10%7D)
![\log _{10}\left(\frac{1}{1 \times 10^{-12} \mathrm{Wm}^{-2}}\right)=1.9](https://tex.z-dn.net/?f=%5Clog%20_%7B10%7D%5Cleft%28%5Cfrac%7B1%7D%7B1%20%5Ctimes%2010%5E%7B-12%7D%20%5Cmathrm%7BWm%7D%5E%7B-2%7D%7D%5Cright%29%3D1.9)
When log goes to other side, express in 10 to the power of that side value,
![\left(\frac{I}{1 \times 10^{-12} W m^{-2}}\right)=10^{1.9}](https://tex.z-dn.net/?f=%5Cleft%28%5Cfrac%7BI%7D%7B1%20%5Ctimes%2010%5E%7B-12%7D%20W%20m%5E%7B-2%7D%7D%5Cright%29%3D10%5E%7B1.9%7D)
![I=1 \times 10^{-12} \mathrm{Wm}^{-2} \times 10^{1.9}=1 \times 10^{-12-1.9}=1 \times 10^{-10.1} \mathrm{Wm}^{-2}](https://tex.z-dn.net/?f=I%3D1%20%5Ctimes%2010%5E%7B-12%7D%20%5Cmathrm%7BWm%7D%5E%7B-2%7D%20%5Ctimes%2010%5E%7B1.9%7D%3D1%20%5Ctimes%2010%5E%7B-12-1.9%7D%3D1%20%5Ctimes%2010%5E%7B-10.1%7D%20%5Cmathrm%7BWm%7D%5E%7B-2%7D)
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