Answer:
L = 9.91 decibels.
Step-by-step explanation:
The loudness, L is inversely proportional to the square of the distance, d, from the source of the sound.
i.e L [tex]\alpha[/tex] [tex]\frac{1}{d^{2} }[/tex]
L = [tex]\frac{k}{d^{2} }[/tex]
Where k is the constant of proportionality.
When d = 14 feet and L = 85 dB, then;
k = L x [tex]d^{2}[/tex]
= 85 x [tex](14)^{2}[/tex]
= 16660
k = 16660
L = [tex]\frac{16660}{d^{2} }[/tex]
Thus, when d = 41 feet, then;
L = [tex]\frac{16660}{(41)^{2} }[/tex]
= [tex]\frac{16660}{1681}[/tex]
= 9.91077
L = 9.91 dB
The loudness is 9.91 decibels.
