Question

The 12 musical notes are given as \( C, C^\#, D, D^\#, E, F, F^\#, G, G^\#, A, A^\#, B \). Frequency of each note is \( \sqrt[12]{2} \) times the frequency of the previous note. If the frequency of the note C is 130.8 Hz, then the ratio of frequencies of notes F# and C is:

• A. \( \sqrt{6} \)
• B. \( \sqrt{2} \)
• C. \( 4\sqrt{2} \)
• D. \( 2 \)

Hint:

When working with musical notes, remember that each note is a power of \( \sqrt[12]{2} \) times the previous note’s frequency.

Answer 1

The Correct Option is B

Step 1: Using the given condition that each frequency is \( \sqrt[12]{2} \) times the frequency of the previous note.

The ratio of the frequencies of any two notes can be expressed as:
\[ \text{Frequency ratio} = \left( \sqrt[12]{2} \right)^n \] where \( n \) is the number of steps between the two notes.

Step 2: Finding the ratio of frequencies of F\# and C.

Since F# is 6 steps away from C in the sequence, we have:
\[ \text{Ratio of frequencies of F\# and C} = \left( \sqrt[12]{2} \right)^6 = \sqrt{2}. \]