The following formula represents the exposure duration in minutes such that noise at x dBA for T(x) minutes or longer becomes hazardous (NIOSH 1998, 1-2). I will refer to T(x) values as T-durations.
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Expression 10: "T" left parenthesis, "x" , right parenthesis equals StartFraction, 480 Over 2 Superscript, StartNestedFraction, left parenthesis, "x" minus 85 , right parenthesis NestedOver 3 , EndNestedFraction , Baseline , EndFractionTx=4802x−853
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We can compose the two functions to obtain the T-duration as a function of being x metres away from a source that is D decibels loud at 1 metre away.
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Expression 12: "S" left parenthesis, "x" , right parenthesis equals "T" left parenthesis, "L" Subscript, "D" , Baseline left parenthesis, "x" , right parenthesis , right parenthesisSx=TLDx
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Here is another slider one can use to play with the number of metres and see specific values of the decibels and T-durations, respectively.
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Expression 14: "a" equals 1a=1
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100100
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Expression 15: "L" Subscript, "D" , Baseline left parenthesis, "a" , right parenthesisLDa
equals=
115115
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Expression 16: "S" left parenthesis, "a" , right parenthesisSa