Chapter 16, Problem 71A

To determine

Tocompare:The number of octavescorresponding to the human hearing range to the number of octaves in the human vision range.

Answer to Problem 71A

There are totally $\text{10}$ octaves correspond to the human hearing range andless than $\text{1}$ octave correspond to human vision range.

Explanation of Solution

Introduction:

An octave in music is a doubling of frequency. That is, an interval in music in which the sound wave vibrational frequency of the lower note is half of its higher note.

Human ear can hear a sound waves of frequency ranging $\text{20 - 20,000 Hz}$ . An octaves for this range of frequency can be written as,

  $\text{20 - 40 Hz, }$

  $\text{40 - 80 Hz, }$

  $\text{80 - 160 Hz,}$

  $\text{160 - 320 Hz,}$

  $\text{320 - 640 Hz,}$

  $\text{640 - 1280 Hz, }$

  $\text{1280 - 3160 Hz, }$

  $\text{3160 - 6320 Hz,}$

  $\text{6320 - 12640 Hz,}$

  $\text{12640 - 20,000 Hz,}$

Thus, there are totally $\text{10}$ octaves correspond to the human hearing range.

Human eye can detect the light waves of frequency ranging $\text{430 - 790 THz}$ .

Double of $\text{430 Hz}$ is $\text{860 Hz}$ which is larger than the upper limit frequency of human eye vision range.

Thus, there is less than $\text{1}$ octave correspond to human vision range.

Conclusion:

There are totally $\text{10}$ octaves correspond to the human hearing range and less than $\text{1}$ octave correspond to human vision range.