The sound from a loud speaker has an intensity level of 80 db at a distance of 2.0m. Consider the speaker to be a point source, how far from

Question

The sound from a loud speaker has an intensity level of 80 db at a distance of 2.0m. Consider the speaker to be a point source, how far from the speaker will the sound have an intensity level of 40 db.

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Thạch Thảo 4 years 2021-07-20T09:53:37+00:00 1 Answers 24 views 0

Answers ( )

  1. Sigrid
    0
    2021-07-20T09:54:44+00:00
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    Answer:

    2.83m

    Explanation:

    The information that we have is

    Intensity at 2.0 m: I=80dB and r_{1}=2m

    we need an intensity level of: I_{2}=40dB

    thus, we are looking for the distance r_{2}.

    which we can find with the law for intensity and distance:

    (\frac{r_{2}}{r_{1}} )^2=\frac{I_{1}}{I_{2}}

    we solve for r_{2}:

    \frac{r_{2}}{r_{1}}=\sqrt{\frac{I_{1}}{I_{2}} }\\\\r_{2}=r_{1}\sqrt{\frac{I_{1}}{I_{2}} }

    and we substitute the known values:

    r_{2}=(2m)\sqrt{\frac{80dB}{40dB} }\\\\r_{2}=(2m)\sqrt{2}\\ r_{2}=2.83m

    at a distance of 2.83m the intensity level is 40dB

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