To find the ratio of the notes G to D, follow these steps:
1. Identify the frequencies of the notes G and D from the given table. From the table:
- The frequency of G = 1568 Hz
- The frequency of D = 1175 Hz
2. Calculate the ratio of G to D by dividing the frequency of G by the frequency of D. This will give us the raw, exact ratio:
[tex]\[
\text{Ratio} = \frac{G}{D} = \frac{1568}{1175} \approx 1.334468085106383
\][/tex]
3. Round the calculated ratio to two decimal places:
[tex]\[
\text{Ratio (to two decimal places)} \approx 1.33
\][/tex]
4. To express this ratio in an integer form, we simplify the fraction [tex]\(\frac{1568}{1175}\)[/tex].
After simplification, we find that the equivalent fraction is:
- Numerator: 1568
- Denominator: 1175
Thus, the integer form of the ratio is [tex]\(\frac{1568}{1175}\)[/tex].
Therefore, the detailed solution is:
- The exact ratio of G to D is approximately 1.334468085106383.
- The ratio rounded to two decimal places is 1.33.
- The ratio in integer form is [tex]\(\frac{1568}{1175}\)[/tex].
Among the provided options ([tex]\(\frac{5}{4}\)[/tex], [tex]\(\frac{4}{3}\)[/tex], [tex]\(\frac{3}{2}\)[/tex], and [tex]\(\frac{2}{1}\)[/tex]), none of them represent the same ratio as 1.33 or [tex]\(\frac{1568}{1175}\)[/tex].
Thus, there is no exact match among the given options for the ratio of G to D as found from the provided frequencies.
