To find the ratio of the frequency of note F to note C and express it in both decimal and integer-ratio forms, follow these steps:
1. Identify the frequencies from the table:
- Frequency of F = 1397 Hz
- Frequency of C = 1047 Hz
2. Calculate the ratio:
- The ratio of the frequency of F to the frequency of C is calculated by dividing the frequency of F by the frequency of C:
[tex]\[
\text{Ratio} = \frac{\text{Frequency of F}}{\text{Frequency of C}} = \frac{1397}{1047}
\][/tex]
3. Compute the decimal value of the ratio:
- Using a calculator, divide 1397 by 1047 to get the decimal value:
[tex]\[
\text{Ratio} \approx 1.3342884431709647
\][/tex]
4. Express the decimal ratio in integer-ratio form:
- To convert the decimal ratio to an integer-ratio form, we compare the calculated ratio to the given integer ratios. Specifically:
- [tex]\(\frac{3}{2} \approx 1.5\)[/tex]
- [tex]\(\frac{4}{3} \approx 1.3333\)[/tex]
- [tex]\(\frac{5}{4} \approx 1.25\)[/tex]
- [tex]\(\frac{2}{1} = 2\)[/tex]
- The calculated ratio of 1.3342884431709647 is very close to [tex]\(\frac{4}{3}\)[/tex] (which is approximately 1.3333). Therefore, we can express the ratio as [tex]\(\frac{4}{3}\)[/tex] in integer-ratio form.
5. Conclusion:
- The ratio of the frequency of note F to note C, calculated to two decimal places, is approximately 1.33.
- Expressed in integer-ratio form, this ratio is [tex]\(\frac{4}{3}\)[/tex].
Thus, the answer is:
[tex]\[ \frac{4}{3} \][/tex]
