Chapter 12, Problem 66GP

To determine

To Find: The octaves that are available in the human audible range approximately.

Answer to Problem 66GP

The total number of octaves that are available in audible range are $10$ .

Explanation of Solution

Introduction:

The lowest frequency that a human can hear is approximately $20\text{ Hz}$ and the highest frequency (upper limit) that the human can hear is nominally $20000\text{ Hz}\left(20\text{ kHz}\right).$

To know number of octaves, avery simple approach is used to divide $20000\text{ Hz}$ repeatedly to reach the lower limit that the human can hear (lower frequency). The number of times the division can be carried out to reach the lower frequency that can be heard by human is the number of octaves.

  $\begin{array}{l}20000\text{ Hz}÷2=10000\text{ Hz}\\ 10000\text{ Hz}÷\text{2 = 5000 Hz}\\ \text{5000 Hz}÷\text{2}=2500\text{ Hz}\\ 2500\text{ Hz}÷2=1250\text{ Hz}\\ 1250\text{ Hz}÷2=625\text{ Hz}\\ 625\text{ Hz}÷2=312.5\text{ Hz}\\ 312.5\text{ Hz}÷2=156.25\text{ Hz}\\ 156.25\text{ Hz}÷2=78.125\text{ Hz}\\ 78.125\text{ Hz}÷2=39.06\text{ Hz}\\ 39.06\text{ Hz}÷2=19.53\text{ Hz}\end{array}$

Therefore, the total number of octaves that are available in audible range are $10$ .

Conclusion:

Ten (10) octaves that are available in the human audible range approximately.