lprandolph007
Answered

Using the table, find the ratio of the following notes to two decimal places. Then express your answer in integer-ratio form.

\begin{tabular}{|ccccccccccccc|}
\hline A & A\# & B & C & C\# & D & D\# & E & F & F\# & G & G\# & A \\
\hline 880 & 932 & 988 & 1,047 & 1,109 & 1,175 & 1,245 & 1,319 & 1,397 & 1,480 & 1,568 & 1,661 & 1,760 \\
\hline
\end{tabular}

Find the ratio of [tex]$G$[/tex] to [tex]$D$[/tex].
A. [tex]$\frac{5}{4}$[/tex]
B. [tex]$\frac{4}{3}$[/tex]
C. [tex]$\frac{3}{2}$[/tex]
D. [tex]$\frac{2}{1}$[/tex]



Answer :

GinnyAnswer
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.

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