Question

The tones that are separated by three octaves have a frequency ratio of
A) $8$
B) $16$
C) $3$
D) $6$

Answer 1

Hint:Octave is a logarithmic unit for ratios between frequencies. Each octave has double frequency as compared to the previous octave. Consider the first octave has a ratio of frequency as $2:1$ . Then find the frequency of the second octave and thus the third octave. Then find the required frequency ratio.

Complete step by step solution:Octaves is the term related to electronics as well as to music. In musical scale an octave means doubling of the frequency. In electronics, an octave is the logarithmic unit for ratios between two frequencies.
We know that each octave is double of the previous octave. Let the first octave have frequency in the ratio

$2f:1f$

Here $f$ is the frequency. Thus, the second octave will be double of it, that is $4f:2f$ . Similarly, for the third octave, it will be double of the second octave. Therefore, the third octave will be $8f:4f$ .
The frequency ratio will be given as:

$\dfrac{{8f}}{f} = 8$

Therefore, the tones that are separated by three octaves have a frequency ratio of $8:1$ or $8$ .

Hence, option A is the correct option.

Note:In musical intervals, when the frequency ratio of the tone is in the ratio $2:1$ , then the musical interval is known as an octave. Similarly, the second octave will be double of this octave and the third octave will be double of the second octave. When the frequency ratio is $3:2$ , the music interval is known as perfect fifths. And when the frequency ratio is $5:4$ , the music interval is known as the major third.