Sound Intensity and Decibels

Sound intensity (I) is defined as the acoustic power (P) transferred per unit area in a specific direction. For an isotropic source in a free field (where there are no reflections), the power spreads spherically, meaning the intensity decreases with the square of the distance (r) from the source: I = P / (4πr2).

Experiment: Inverse-Square and Multi-Source Addition

Use the interactive Sound Intensity and Decibels module to explore these effects:

1. Set the Power per source P to "1" (mW).
2. Set the Distance r to "1" (m) and Incoherent source count N to "1". Observe the baseline intensity level (~79.0079 dB).
3. Double the distance by setting Distance r to "2". Notice the intensity drops to one quarter, and the level decreases by exactly ~6.02 dB (which is 20 log₁₀(2)).
4. Return Distance r to "1", and increase the Incoherent source count N to "10". Observe that 10 times the intensity results in exactly a +10 dB increase in the level (~89.0079 dB).
5. Set the Power per source P to "0" (mW) to see the limit case where the logarithmic level drops to "minus infinity".
6. Restore Power per source P to 1, Distance r to 1 and Incoherent source count N to 1. The combined and single-source comparison readouts are both shown and match exactly.
7. Set Distance r to 0. The real domain error appears and intensity/level readouts disappear. Restore 1, then clear Incoherent source count N, observe its integer error and restore 1.
8. Set Power per source P to 1000, Distance r to 20 and Incoherent source count N to 10. The finite intensity is about 0.00198943678865 W/m² and level about 92.9873014465 dB.