The tones that are separated by three octaves have a frequency ratio of

Options

A. 3
B. 6
C. 8
D. 16

Answer

To find the frequency ratio of two tones that are separated by three octaves, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of an Octave**:
An octave is defined as the interval between one musical pitch and another with double its frequency. This means if one tone has a frequency \( f \), then the tone one octave higher has a frequency of \( 2f \).

2. **Determine the Relationship for Multiple Octaves**:
If two tones are separated by \( n \) octaves, the frequency of the higher tone can be expressed in terms of the lower tone's frequency. For three octaves, if the lower tone has a frequency \( f_2 \), the higher tone \( f_1 \) can be expressed as:
\[ f_1 = 2^n \cdot f_2 \]
where \( n \) is the number of octaves. In this case, \( n = 3 \).

3. **Substitute the Value of n**:
Substitute \( n = 3 \) into the equation:
\[ f_1 = 2^3 \cdot f_2 \]

4. **Calculate \( 2^3 \)**:
Calculate \( 2^3 \):
\[ 2^3 = 8 \]
Therefore, we have:
\[ f_1 = 8 \cdot f_2 \]

5. **Find the Frequency Ratio**:
To find the frequency ratio \( \frac{f_1}{f_2} \):
\[ \frac{f_1}{f_2} = 8 \]

### Conclusion:
The frequency ratio of two tones that are separated by three octaves is \( 8:1 \).