Question: (I) Estimate the number of octaves in the human audible range, 20 Hz to 20 kHz.

The doubling of frequency corresponds to one octave. The higher frequency will have the frequency two times the lower frequency for an octave.

The minimum human audible range of hearing is\({f_1} = 20\;{\rm{Hz}}\).

The maximum human audible range of hearing is \({f_2} = 20\;{\rm{kHz}}\).

The number of octaves in the human audible range is calculated as:

\(\frac{{{f_1}}}{{{f_2}}} = {2^n}\)

Here, n is the number of octaves.

Substitute the values in the above relation.

\(\begin{array}{c}\frac{{20{\rm{ kHz}}\left( {\frac{{1000\;{\rm{Hz}}}}{{1\;{\rm{kHz}}}}} \right)}}{{20{\rm{ Hz}}}} = {2^n}\\1000{\rm{ Hz}} = {2^n}\\n = \frac{{\log \left( {1000{\rm{ Hz}}} \right)}}{{\log 2}}\\ \approx 10\end{array}\)

The number of octaves in \(20{\rm{ Hz}}\) to \(20{\rm{ kHz}}\) range is 10.