Given a loudspeaker with a rated sensitivity of 85 dB SPL, what power tap should be selected to achieve a target sound pressure level of 75 dB SPL in a space located 3 m away?

To determine the appropriate power tap for achieving a target sound pressure level (SPL) of 75 dB SPL at a distance of 3 meters when starting with a loudspeaker sensitivity of 85 dB SPL, it's essential to understand the relationship between power, distance, and sound levels.

The sensitivity of a loudspeaker (85 dB SPL) indicates the sound pressure level it produces when provided with a specific amount of power (typically 1 watt) at a distance of 1 meter. Since the goal is to achieve a lower SPL (75 dB SPL) at 3 meters, we must first account for the effects of distance on sound propagation.

As sound travels, it dissipates due to the inverse square law, which states that sound intensity decreases by approximately 6 dB for every doubling of distance from the source. From 1 meter to 3 meters, there are two doublings (1m to 2m and 2m to 4m), resulting in a theoretical decrease of about 12 dB (6 dB for each doubling).

Starting with the speaker's sensitivity of 85 dB at 1 meter, after accounting for the distance:

1. At 1 meter, you have 85