A certain loudspeaker system emits sound isotropically (uniformly in all directions) with a frequency of 1,054 Hz and an intensity of 6.429

Question

A certain loudspeaker system emits sound isotropically (uniformly in all directions) with a frequency of 1,054 Hz and an intensity of 6.429 mW/m2 at a distance of 7.945 m. Assume that there are no reflections. What is the intensity in 10-3 W/m2 at 39.3 m? (you don’t need to write the power/prefix and unit

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Calantha 4 months 2021-07-28T14:52:23+00:00 1 Answers 0 views 0

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    2021-07-28T14:54:19+00:00

    Answer:

    The intensity in 10-3 W/m2 at 39.3 m is 0.26275*10^{-3}\ W/m^2

    Explanation:

    Given Data:

    frequency=1,054 Hz

    intensity=6.429 mW/m^2

    distance=7.945 m.

    Required:

    intensity in 10^-3 W/m^2 at 39.3 m=?

    Solution:

    Intensity at distance r from point source which is emitting sound waves of power P is given by the following formula:

    Intensity=I=\frac{P}{4\pi r^2}

    Where:

    P is the power

    r is the distance

    \frac{I_1}{I_2}=\frac{\frac{P}{4\pi r_1^2}}{\frac{P}{4\pi r_2^2}}  \\\frac{I_1}{I_2}=\frac{r_2^2}{r_1^2} \\I_2=I_1*\frac{r_1^2}{r_2^2}

    r_1= 7.945 m\\r_2= 39.3 m\\I_2=6.429*10^{-3} *\frac{7.945^2}{39.3^2}

    I_2=0.00026275\ W/m^2\\I_2=0.26275*10^{-3}\  W/m^2

    The intensity in 10^-3 W/m2 at 39.3 m is 0.26275*10^{-3}\ W/m^2

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