Question

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

Answer 1

Answer:

Step-by-step explanation:

If two variables are inversely proportional, it means that an increase in the value of one variable would cause a corresponding decrease in the other variable. Also, a decrease in the value of one variable would cause a corresponding increase in the other variable.

Given that loudness, L varies inversely with the square of the distance, d², if we introduce a constant of proportionality, k, the expression becomes

L = k/d²

If L = 60 when d = 8, then

60 = k/8² = k/64

k = 60 × 64 = 3840

Therefore, the inverse variation equation is

L = 3840/d²

When d = 41, then

L = 3840/41²

L = 2.28 decibels

Answer 2

Answer:

The jetski is 2.28 dB loud when the person is 41 feet away.

Step-by-step explanation:

Loudness (L) ∝ 1 / Distance² (d²)

Introduce a constant 'K'

L = K (1/d²)

L = K/d²

K = Ld²

Find the K from a previously known information: If a person 8 feet from a jetski hears 60 decibels loud

∴ d = 8 ft , L = 60 db

K = 60(8²) = 3840

How loud is the jetski when the person is 41 feet away?

Distance is now 41 ft

since: L = K/d²

∴ L = 3840 / 41²

L = 3840 / 1681

L = 2.28 db