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21 October, 10:35

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 8 feet from a jetski, it is 60 decibels loud.

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

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Answers (2)
  1. 21 October, 11:01
    0
    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
  2. 21 October, 12:57
    0
    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
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