Two tuning forks $A$ and $B$ produce notes of frequencies $258 ext{ Hz}$ and $262 ext{ Hz}$. An unknown note sounded with $A$ produces certain beats. When the same note is sounded with $B$, the beat frequency gets doubled. The unknown frequency is [KCET 2011]

Question

Two tuning forks $A$ and $B$ produce notes of frequencies $258	ext{ Hz}$ and $262	ext{ Hz}$. An unknown note sounded with $A$ produces certain beats. When the same note is sounded with $B$, the beat frequency gets doubled. The unknown frequency is [KCET 2011]

Aicharya · Accepted Answer

Given, $n_A = 258	ext{ Hz}$ and $n_B = 262	ext{ Hz}$ If it produces $x$ beats with 258 and $2x$ with 262, then $262 - (258 - x) = 2x$ $\Rightarrow 262 - 258 + x = 2x \Rightarrow x = 4$ Therefore, unknown frequency, $n = 258 - x = 254	ext{ Hz}$

Two tuning forks $A$ and $B$ produce notes of frequencies $258\text{ Hz}$ and $262\text{ Hz}$. An unknown…

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