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The sound intensity is 0.18 mW m^{-2} at a distance of 3 m in any direction from a source of sound - Leaving Cert Physics - Question 10 - 2022

Question 10

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The sound intensity is 0.18 mW m^{-2} at a distance of 3 m in any direction from a source of sound. Calculate the power of the source.

Worked Solution & Example Answer:The sound intensity is 0.18 mW m^{-2} at a distance of 3 m in any direction from a source of sound - Leaving Cert Physics - Question 10 - 2022

Step 1

Calculate Area (A)

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Answer

To find the power of the sound source, we first need to calculate the area over which the sound intensity is measured. The area for a spherical distribution is given by the formula:

$A = 4\pi r^2$

Substituting the distance, r = 3 m:

$A = 4\pi (3^2) = 4\pi (9) = 36\pi \approx 113.1 \text{ m}^2$

Step 2

Calculate Power (P)

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Answer

Now, we use the relationship between power, intensity, and area:

$P = I \times A$

Where:

P = power
I = intensity = 0.18 , \text{mW m}^{-2} = 0.18 \times 10^{-3} , \text{W m}^{-2}
A = area calculated previously

Substituting the values:

$P = 0.18 \times 10^{-3} \times 113.1$

Calculating the power:

$P \approx 0.02034 \text{ W} \approx 0.02 \text{ W}$

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