For a reference sound pressure of 2×10⁻⁵ N m⁻², the sound level measured at the operator's workspace of a tractor was 80 dB. If the RMS sound pressure is increased by eight times, the resulting sound pressure level in dB, will be _____.
Official Answer Key:
98.0 to 98.2
Step-by-Step Solution & Explanation
Sound pressure level relates to pressure ratio as L = 20 log₁₀(p/pᵣₑf). Increasing RMS pressure 8× changes L by:
ΔL = 20 log₁₀(8) = 20 × 0.9031 = 18.06 dB.
New sound level = 80 + 18.06 = 98.06 dB. This lies within the accepted range 98.0–98.2.
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