Question

The loudness, L, of a sound (measured in decibels, dB) is inversely proportional to the square of the distance, d

Answer 1

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 $\alpha$ $\frac{1}{d^{2} }$

L = $\frac{k}{d^{2} }$

Where k is the constant of proportionality.

When d = 14 feet and L = 85 dB, then;

k = L x $d^{2}$

  = 85 x $(14)^{2}$

 = 16660

k = 16660

L = $\frac{16660}{d^{2} }$

Thus, when d = 41 feet, then;

L = $\frac{16660}{(41)^{2} }$

  = $\frac{16660}{1681}$

  = 9.91077

L = 9.91 dB

The loudness is 9.91 decibels.