Respuesta :
Answer:
Positions of two points are : 3.4 m and 4.3 m.
Explanation:
Let two distance be r and r+0.94.
Now intensity at r, [tex]I_{1\\}[/tex] = [tex]\frac{P}{4 \pi r^{2} }[/tex]
intensity at (r+0.94), [tex]I_{2}[/tex] = [tex]\frac{P}{4 \pi (r+0.94)^{2} }[/tex]
Now for decibel,
[tex]B_{1}[/tex] = 10 log ([tex]\frac{I_{1} }{I_{0} }[/tex])
[tex]B_{2}[/tex] = 10 log ([tex]\frac{I_{2} }{I_{0} }[/tex])
As given on question:
[tex]B_{1}[/tex] - [tex]B_{2}[/tex] = 2.12 dB
⇒ 2.12 dB = 10 log ([tex]\frac{I_{1} }{I_{0} }[/tex]) - 10 log ([tex]\frac{I_{2} }{I_{0} }[/tex])
⇒0.212 = log ([tex]\frac{I_{1} }{I_{2} }[/tex])
⇒ [tex]\frac{I_{1} }{I_{2} }[/tex] = [tex]10^{0.212}[/tex]
⇒ [tex]\frac{(r+0.94)^{2} }{r^{2} }[/tex] = [tex]10^{0.212}[/tex]
⇒ [tex]\frac{r+0.94}{r}[/tex] = [tex]10^{0.106}[/tex]
⇒ r= 3.4 m, r+0.94= 4.3 m
Hence the position of two points is 3.4 m and 4.3 m.
