An acoustical application of the logarithmic transformation to a normally distributed random variable

The logarithmic transformation,
Y=a \log X
, of the normally distributed random variable
X
is discussed in this paper. Particular attention is focused on the field of acoustical noise measurements. The probability density function, mean value, and standard deviation of
Y
are derived, and a graphical method for estimating its 95th and 97.72nd percentiles is presented.