Question

what will be the frequency ratio of the tones which are separated by three octaves?
$\begin{align}
  & A.8 \\
 & B.16 \\
 & C.3 \\
 & D.6 \\
\end{align}$

Answer 1

Hint: Any two sounds which are having the frequency made to be in a $2:1$ ratio are known to be separated by an octave. An octave is defined as the distance between one note and another note which has its frequency twice of the first one. Octaves have great importance in the context of music. This all will help you in answering this question.

Complete answer:
An octave is basically a musical interval. An octave can be explained both in terms of music and in terms of physics also. In terms of music we can define octave as the distance between one note and the next note carrying its similar name. In terms of physics we can define octave as the distance between one note and another note that is having its frequency twice of the first one. That is we can say that, any two sounds which have frequencies making a $2:1$ ratio are defined to be separated by an octave. Therefore we can say that, as per the question, when the tones that are separated by three octaves, they will be having a ratio of the frequency given as,
$f=2\times 2\times 2=8$
Therefore the frequency ratio of the three octaves have been obtained.

So, the correct answer is “Option A”.

Note:
If we are moving upwards by one interval at a time, then it has to be understood that we are advancing in half steps. This is known as semitones. If we are moving downwards by two intervals at a time, then it has to be clear that it is advancing in whole steps. They are also known as whole tones.