Respuesta :
Answer:
A)
665.5 W
B)
575.5 m
Explanation:
A)
[tex]S[/tex] = Sound level registered = 128 dB
[tex]I_{o}[/tex] = Intensity at reference level = [tex]1\times10^{-12}[/tex] Wm⁻²
[tex]I[/tex] = Intensity at the location of meter
Sound level is given as
[tex]S = 10 log_{10}\left ( \frac{I}{I_{o}} \right )[/tex]
[tex]128 = 10 log_{10}\left ( \frac{I}{1\times10^{-12}} \right )\\12.8 = log_{10}\left ( \frac{I}{1\times10^{-12}} \right )\\10^{12.8} = \frac{I}{1\times10^{-12}} \right \\I = 6.3[/tex]
[tex]P[/tex] = power output of the speaker
[tex]r[/tex] = distance from the speaker = 2.9 m
Power output of the speaker is given as
[tex]P = I(4\pi r^{2} )\\P = (6.3) (4) (3.14) 2.9^{2}\\P = 665.5 W[/tex]
B)
[tex]S[/tex] = Sound level = 82 dB
[tex]I_{o}[/tex] = Intensity at reference level = [tex]1\times10^{-12}[/tex] Wm⁻²
[tex]I[/tex] = Intensity at the location of meter
Sound level is given as
[tex]S = 10 log_{10}\left ( \frac{I}{I_{o}} \right )[/tex]
[tex]82 = 10 log_{10}\left ( \frac{I}{1\times10^{-12}} \right )\\8.2 = log_{10}\left ( \frac{I}{1\times10^{-12}} \right )\\10^{8.2} = \frac{I}{1\times10^{-12}} \right \\I = 1.6\times10^{-4}Wm^{-2}[/tex]
Power of the speaker is given as
[tex]P = I(4\pi r^{2} )\\665.5 = (1.6\times10^{-4}) (4) (3.14) r^{2}\\r = 575.5 m[/tex]
