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The loudness, L, of a sound (measured in decibels, dB) is inversely proportional to the square of the distance, d
from the source of the sound.
A person 14 feet from a jetski, it is 85 decibels loud.
How loud is the jetski when the person is 41 feet away? (Round to 3 decimal places.)
dB

Sagot :

olayemiolakunle65

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.

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