The intensity of the sound wave from an airplane is 1.0 × 10^2 W/m^2 at 6 m. What is the intensity at 97 m?

Question

The intensity of the sound wave from an airplane is 1.0 ×
10^2 W/m^2 at 6 m. What is the intensity at 97 m?

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Diễm Thu 3 years 2021-08-04T05:24:41+00:00 1 Answers 15 views 0

Answers ( )

  1. niczorrrr
    0
    2021-08-04T05:26:01+00:00
    Reply

    Answer:

    0.38 W/m^2

    Explanation:

    A sound wave propagates in all directions radially from its source; therefore, it follows an inverse square law, it means that its intensity decreases inversely proportional to the square of the distance:

    I \propto \frac{1}{r^2}

    where

    I is the intensity

    r is the distance from the source of the wave

    This means that we can rewrite the equation as:

    I_1 r_1^2 = I_2 r_2^2

    where in this problem:

    I_1 = 1.0 \cdot 10^2 W/m^2 is the intensity of the sound wave when the distance is

    r_1 = 6 m

    I_2 is the intensity of the sound wave when the distance is

    r_2 = 97 m

    Solving for I2, we find:

    I_2 = I_1 \frac{r_1^2}{r_2^2}=(1.0\cdot 10^2) \frac{6^2}{97^2}=0.38 W/m^2

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