If the intensity of a sound wave is 10 W/m² at a distance of 5 m from the source, calculate the intensity at a distance of 20 m from the source.
Question
If the intensity of a sound wave is 10 W/m² at a distance of 5 m from the source, calculate the intensity at a distance of 20 m from the source.
Solution
The intensity of a sound wave decreases with the square of the distance from the source. This is known as the inverse square law.
The formula to calculate the intensity at a different distance is:
I2 = I1 * (d1/d2)²
where:
- I1 is the initial intensity (10 W/m² in this case)
- d1 is the initial distance (5 m in this case)
- d2 is the final distance (20 m in this case)
Substituting the given values into the formula, we get:
I2 = 10 W/m² * (5 m / 20 m)²
Solving the equation, we find:
I2 = 10 W/m² * (0.25)² = 10 W/m² * 0.0625 = 0.625 W/m²
So, the intensity of the sound wave at a distance of 20 m from the source is 0.625 W/m².
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