Question

A relatively calm room has background sound power level (SPL) of 30 decibels (dB). A television and a radio with SPL of 80 dB and 70 dB, respectively, started operating simultaneously in this room. Given the reference sound power is $10^{-12}$ Watts, what will be the resulting SPL in the room, assuming all the sources operate independently?

• A. 180.0 dB
• B. 80.4 dB
• C. 82.4 dB
• D. 150.0 dB

Hint:

Sound levels in dB cannot be added directly. Always convert to power, add, then convert back.

Answer 1

The Correct Option is D

Sound levels add using powers, not decibels.
Given SPLs: 30 dB, 80 dB, 70 dB.
Convert each to power ratio:
\[ P = 10^{L/10} \] \[ P_{\text{total}} = 10^{30/10} + 10^{80/10} + 10^{70/10} \] \[ P_{\text{total}} = 10^3 + 10^8 + 10^7 = 1{,}10{,}001{,}000 \approx 1.1 \times 10^8 \] Now convert back to SPL:
\[ L_{\text{total}} = 10 \log_{10}(P_{\text{total}}) \] \[ L_{\text{total}} = 10 \log_{10}(1.1 \times 10^8) \] \[ = 10(8 + \log_{10} 1.1) = 80 + 0.41 = 80.41 \text{ dB} \] Thus the resulting SPL is approximately \(80.4\) dB.
Final Answer: 80.4 dB