The intensity level of a sound is typically measured in decibels (dB) and is calculated using the formula:
Intensity Level (dB) = 10 * log10(I/I0)
Where I is the sound intensity in watts per square meter (W/m²), and I0 is the reference intensity, which is typically set at 10^(-12) W/m².
Let's calculate the intensity level for the given sound intensity of 10^8 W/m²:
Intensity Level = 10 * log10(10^8 / 10^(-12))
Simplifying the logarithm:
Intensity Level = 10 * log10(10^20)
Since log10(10^20) = 20, we can substitute it back:
Intensity Level = 10 * 20
Intensity Level = 200 dB
Therefore, the approximate intensity level of the sound from the radio set at 10^8 W/m² is 200 decibels.