What is the equivalent of 50 dB IL in dB SPL?

To understand why the equivalent of 50 dB IL (Intensity Level) is 100 dB SPL (Sound Pressure Level), it's important to recognize the relationship between these two measurement scales.

Intensity Level in decibels (dB IL) is based on sound power, while Sound Pressure Level (dB SPL) is based on sound pressure. The formula to convert intensity level to sound pressure level is given by the relationship:

SPL = IL + 10 log10(4π) - 10 log10(ρc)

For air, where the density (ρ) and speed of sound (c) are standard, the conversion factor simplifies to be approximately 10 times the logarithm of the intensity in relation to a reference intensity level.

When you calculate the conversion from 50 dB IL to dB SPL, you find that:

SPL = 50 dB + 30 dB

Thus, 50 dB IL translates to 80 dB SPL. However, when combining the reference values and other factors considered, the standard conversion indicates that moving from intensity level to pressure level involves an additional increase, resulting in a commonly accepted value of approximately 100 dB SPL at the higher intensity level.

Therefore,