A standard man shouting loudly produces a 87.4dB sound at a distance of 7.05m. At what rate does he emit sound energy? Express the result in J/s.
To find the rate at which the man emits sound energy, we can use the formula for sound intensity:
Intensity (I) = Power (P) / Area (A)
The sound intensity is measured in watts per square meter (W/m²). In this case, we need to find the power emitted by the man in watts.
First, let's find the area over which the sound spreads. We know the distance from the man, which is 7.05m. Assuming the sound spreads evenly in all directions, the area would be calculated using the formula for the surface area of a sphere:
Area (A) = 4πr²
We substitute the radius into the equation:
A = 4π(7.05m)²
Next, we need to convert the decibel level into Watts per square meter. The dB level is a logarithmic scale, so we need to convert it into linear form using the formula:
Sound Intensity (IL) = 10^(dB/10)
Substituting the given dB level, we find:
IL = 10^(87.4dB/10)
Finally, we can calculate the power emitted by the man using the formula:
Power (P) = Intensity (I) * Area (A)
P = IL x A
Substituting the calculated intensity and area into the equation, we find:
P = (10^(87.4dB/10)) * (4π(7.05m)²)
Simplifying the equation and calculating the result will give us the rate at which the man emits sound energy in watts.