KCET · Physics · Waves and Sound
The frequency of the second overtone of the open pipe is equal to the frequency of the first overtone of the closed pipe. The ratio of the lengths of the open pipe and the closed pipe is
- A \(2: 1\)
- B \(1: 2\)
- C \(1: 3\)
- D \(3: 1\)
Answer & Solution
Correct Answer
(A) \(2: 1\)
Step-by-step Solution
Detailed explanation
The frequency of first overtone for closed pipe,
\(f_{c}=\frac{3 \mathrm{v}}{4 I_{c}}\)
Given, i.e.,
\(\begin{aligned}
f_{c} &=f_{0} \\
\frac{3 v}{4 I_{c}} &=\frac{3 v}{2 I_{o}} \Rightarrow \frac{I_{o}}{I_{c}}=\frac{2}{1}
\end{aligned}\)
\(f_{c}=\frac{3 \mathrm{v}}{4 I_{c}}\)
Given, i.e.,
\(\begin{aligned}
f_{c} &=f_{0} \\
\frac{3 v}{4 I_{c}} &=\frac{3 v}{2 I_{o}} \Rightarrow \frac{I_{o}}{I_{c}}=\frac{2}{1}
\end{aligned}\)
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