Using the sound pressure level (SPL) method of approximating distance and power, calculate the power required to produce 89 dB at 4 m (13.1 ft) with a loud speaker that is rated at a SPL of 95 dB. What input power level (in watts) is required to appropriately power the speaker?
To calculate the power required, we need to use the inverse square law of sound propagation. The sound pressure level decreases by 6 dB every time the distance from the sound source is doubled. Since the speaker is rated at 95 dB at 1 meter, we first calculate the SPL at 4 meters. Going from 1 meter to 4 meters involves two doublings of distance (1m to 2m to 4m), which results in a decrease of 12 dB (6 dB per doubling). Therefore, the SPL at 4 meters would be 95 dB - 12 dB = 83 dB. To achieve 89 dB at 4 meters, we need an additional 6 dB of gain. Doubling the power increases the SPL by 3 dB. Thus, to increase by 6 dB, the power needs to be quadrupled. Starting from 1 watt, we need 4 watts to achieve 89 dB at 4 meters. None of the provided options match this intermediate calculation. However, if we double the power again to achieve a 9 dB increment rather than 6 dB, we reach 8 watts, which is the correct and the next closest higher option in the list.
TDMM page 13-73 (1119) Loudspeaker Power