RCDD · Question #198
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…
The correct answer is C. 4 watts. Applying the inverse square law to a speaker's 1W/1m sensitivity rating determines how much additional input power compensates for distance-related SPL loss.
Question
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?
Options
- A1 watt
- B2 watts
- C4 watts
- D8 watts
How the community answered
(38 responses)- A18% (7)
- B3% (1)
- C71% (27)
- D8% (3)
Why each option
Applying the inverse square law to a speaker's 1W/1m sensitivity rating determines how much additional input power compensates for distance-related SPL loss.
1 watt produces 83 dB at 4m (95 - 12 dB), which falls 6 dB short of the 89 dB target.
2 watts adds only 3 dB over 1W, yielding 86 dB at 4m - still 3 dB below the required 89 dB.
The speaker's sensitivity is 95 dB at 1W/1m. Distance from 1m to 4m represents two doublings, causing a 12 dB drop (6 dB per doubling), yielding 83 dB at 1W. Reaching the 89 dB target requires 6 dB more. Because each 3 dB gain requires doubling power, 6 dB requires 4x power - so 4 watts is correct.
8 watts adds 9 dB over 1W, yielding 92 dB at 4m, which exceeds the target by 3 dB and is more than the minimum required.
Concept tested: Inverse square law loudspeaker power and SPL calculation
Source: https://www.avixa.org/training-certification/certification/cts
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