Answer:
[tex]L = 109.01 db[/tex]
Explanation:
Given
Power, P = 100 W
Distance, d = 10 m
Required
Determine the Sound Level
First, the sound intensity as to be calculated; This is done, as follows;
[tex]I = \frac{P}{4\pi d^2}[/tex]
Substitute for P, d and take π as 3.14
[tex]I = \frac{100}{4 * 3.14 * 10^2}[/tex]
[tex]I = \frac{100}{4 * 3.14 * 100}[/tex]
[tex]I = \frac{100}{1256}[/tex]
[tex]I = 0.0796Wm^{-2}[/tex] --- Approximated
Next is to calculate the Sound Level, as follows
[tex]L = 10 * Log(\frac{I}{I_o})[/tex]
Where [tex]I_o = 10^{-12} Wm^{-2}[/tex]
Substitute for I and Io
[tex]L = 10 * Log(\frac{0.0796}{10^{-12}})[/tex]
[tex]L = 10 * Log(0.0796*10^{12)[/tex]
[tex]L = 10 * Log(0.0796*10^{12)[/tex]
[tex]L = 10 * 10.901[/tex]
[tex]L = 109.01 db[/tex]
Hence, the sound level is 109.01 decibels
