How does the intensity of a sound wave change if the distance from the source is increased by a factor of 4? A. The intensity de

Question

How does the intensity of a sound wave change if the distance from the
source is increased by a factor of 4?
A. The intensity decreases by a factor of 4.
B. The intensity increases to by a factor of 16.
c. The intensity decreases by a factor of 16.
D. The intensity increases by a factor of 4.

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Hải Đăng 4 months 2021-09-05T05:51:47+00:00 1 Answers 3 views 0

Answers ( )

    0
    2021-09-05T05:53:32+00:00

    Answer:

    The new intensity decreases by a factor of 16.

    Explanation:

    The intensity of sound wave is given by :

    I=\dfrac{P}{A}

    P is power

    A is area

    I=\dfrac{P}{4\pi r^2}

    or

    I\propto \dfrac{1}{r^2}, r is distance from the source

    If the distance from the  source is increased by a factor of 4, r’ = 4r

    So,

    I'=\dfrac{1}{r'^2}\\\\I'=\dfrac{1}{(4r)^2}\\\\I'=\dfrac{1}{16}\times \dfrac{1}{r^2}\\\\I'=\dfrac{I}{16}

    So, the new intensity decreases by a factor of 16.

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