KCET · Physics · Waves and Sound
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 \(252 \mathrm{~Hz}\)
- C \(254 \mathrm{~Hz}\)
- D \(256 \mathrm{~Hz}\)
Answer & Solution
Correct Answer
(C) \(254 \mathrm{~Hz}\)
Step-by-step Solution
Detailed explanation
Given, \(n_{A}=258 \mathrm{~Hz}, n_{B}=262 \mathrm{~Hz}\)
If it produces \(x\) beats with 258 and \(2 x\) with \(262 .\)
\(\begin{aligned}262-(258-x) &=2 x \\262-258+x &=2 x \\x &=4 \\n &=254 \mathrm{~Hz}\end{aligned}\)
If it produces \(x\) beats with 258 and \(2 x\) with \(262 .\)
\(\begin{aligned}262-(258-x) &=2 x \\262-258+x &=2 x \\x &=4 \\n &=254 \mathrm{~Hz}\end{aligned}\)
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