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GATE 2025 XH2 (English) – Question 3

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

The 12 musical notes are given as $C, C^{\#}, D, D^{\#}, E, F, F^{\#}, G, G^{\#}, A, A^{\#}$, and $B$. 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:

  1. $\sqrt[6]{2}$
  2. $\sqrt{2}$
  3. $\sqrt[4]{2}$
  4. $2$

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Show answer and explanation

Correct answer: (B) $\sqrt{2}$

Explanation

$F^{\#}$ is 6 notes above C (C#, D, D#, E, F, F#). Each step multiplies the frequency by $2^{1/12}$, so the ratio is $\left(2^{1/12}\right)^6 = 2^{1/2} = \sqrt{2}$.