Q138 / 180 · KCET 2011 · Physics
Two tuning forks $A$ and $B$, produce notes of frequencies $258 \mathrm{~Hz}$ and $262 \mathrm{~Hz}$. 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
- A$250 \mathrm{~Hz}$
- B$252 \mathrm{~Hz}$
- Correct answerC$254 \mathrm{~Hz}$
- D$256 \mathrm{~Hz}$
Solution
Given, $n_{A}=258 \mathrm{~Hz}, n_{B}=262 \mathrm{~Hz}$
If it produces $x$ beats with 258 and $2 x$ with $262 .$
$$
\begin{aligned}
262-(258-x) &=2 x \\
262-258+x &=2 x \\
x &=4 \\
n &=254 \mathrm{~Hz}
\end{aligned}
$$
Hence, the correct answer is option: 'C'.