If the intensity of a person’s voice is 3.6×10−7
W/m2
at a distance of 2.1 m, how much sound
power does that person generate?
Answer in units of W
To calculate the sound power generated by a person, you need the intensity of their voice and the distance from which it is measured. The formula to calculate sound power is:
Sound Power (P) = Intensity (I) × Area (A)
Since we only have the intensity and distance, we first need to calculate the area using the formula:
Area (A) = 4πr²
Given:
Intensity (I) = 3.6 × 10^(-7) W/m^2
Distance (r) = 2.1 m
Step 1: Calculate the Area
Area (A) = 4πr²
Area (A) = 4 × π × (2.1 m)²
Using the value of π (pi) as approximately 3.14159, we can calculate the area:
Area (A) ≈ 4 × 3.14159 × (2.1 m)²
Step 2: Calculate Sound Power (P)
Sound Power (P) = Intensity (I) × Area (A)
Substituting the given values:
Sound Power (P) = (3.6 × 10^(-7) W/m²) × Area (A)
We'll now substitute the value of Area (A) into the equation and calculate the Sound Power:
Sound Power (P) ≈ (3.6 × 10^(-7) W/m²) × (4 × 3.14159 × (2.1 m)²)
Calculating the expression inside the parentheses first:
Sound Power (P) ≈ (3.6 × 10^(-7) W/m²) × (4 × 3.14159 × 4.41 m²)
Multiplying the numbers:
Sound Power (P) ≈ 5.52364 × 10^(-5) W/m² × 55.2068 m²
Finally, multiplying the remaining numbers:
Sound Power (P) ≈ 0.00304839 W
Therefore, the person generates approximately 0.00304839 W of sound power.