Subtopic: Human engineering and safety considerations in design of tractor and agricultural implements
Question Statement:
An accelerator mounted to the waist of a seated tractor operator records an RMS acceleration of 2.5 m·s⁻². By improving the seat design, the vibration acceleration level is decreased by 5 dB. After improvement, the RMS acceleration, in m·s⁻², is __________. (Rounded off to 3 decimal places)
Official Answer Key:
1.300 to 1.500
Step-by-Step Solution & Explanation
Vibration acceleration level is an amplitude-type quantity, so the decibel definition uses the factor 20:
L = 20 log₁₀(a/a_ref) dB
A reduction of 5 dB means:
20 log₁₀(a₂/a₁) = −5
log₁₀(a₂/a₁) = −0.25
a₂/a₁ = 10^(−0.25) = 0.56234
Therefore:
a₂ = 2.5 × 0.56234 = 1.406 m·s⁻²
Key distinction: using 10 log₁₀ (the power/energy convention) would wrongly give 2.5 × 0.3162 = 0.79 m·s⁻². Acceleration, like sound pressure, is an amplitude quantity and takes 20 log₁₀.
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