A 75% dose is equivalent to 87.9 dB True False A 75% dose is equivalent to 87.9 dB

A 75% dose is equivalent to 87.9 dB True False A 75% dose is equivalent to 87.9 dB

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The correct answer and explanation is:

Correct Answer: True

A 75% dose is equivalent to 87.9 decibels (dB) True, based on the logarithmic relationship between noise dose percentages and sound levels. This concept is most commonly applied in occupational safety and health standards, particularly those set by organizations like the Occupational Safety and Health Administration (OSHA) and the National Institute for Occupational Safety and Health (NIOSH).

In occupational settings, a noise “dose” represents the amount of sound energy a person is exposed to during a workday relative to a standard permissible limit. For instance, OSHA considers a full 100% dose to be the maximum allowable noise exposure for an 8-hour workday, corresponding to 90 dB with a 5 dB exchange rate. This exchange rate means for every increase of 5 dB, the allowable exposure time is cut in half.

Using the OSHA formula or a noise dose chart, a 75% noise dose corresponds approximately to a time-weighted average (TWA) of 87.9 dB. This is not calculated by a simple proportion because the decibel scale is logarithmic. The relationship between dose percentage and dB level is non-linear.

The dose percentage can be related to decibels using this formula: TWA=16.61log⁡10(D100)+90TWA = 16.61 \log_{10} \left(\frac{D}{100}\right) + 90

Where D is the dose percentage.

Substitute 75 for D: TWA=16.61log⁡10(0.75)+90≈16.61(−0.1249)+90≈−2.07+90=87.93 dBTWA = 16.61 \log_{10}(0.75) + 90 \approx 16.61 (-0.1249) + 90 \approx -2.07 + 90 = 87.93 \, dB

This confirms that a 75% dose equates to roughly 87.9 dB, supporting the statement as true. Understanding this relationship is essential in managing workplace hearing conservation programs and ensuring compliance with noise exposure standards.