MHT CET · Physics · Waves and Sound
An organ pipe \(\mathrm{P}_1\) closed at one end has vibrating air column in its first overtone and another pipe \(\mathrm{P}_2\) open at both ends has vibrating air column in the third overtone, which are in resonance with a given tuning fork. The ratio of the length of pipe \(P_1\) to that of \(P_2\) is
- A 3:8
- B 1:2
- C 1:8
- D 5:8
Answer & Solution
Correct Answer
(A) 3:8
Step-by-step Solution
Detailed explanation
Since, both pipes are in resonance with a given tuning fork, therefore, they will have the same frequency of vibration.
For the organ pipe closed at one end.
First overtone \((n=3)\), .
For organ pipe open at both ends,
Third overtone \((n=4)\),
From (1) and (2)
\(\begin{aligned}
& \frac{3 v}{4 l_1}=\frac{4 v}{2 l_2} \\
& \Rightarrow \frac{l_1}{l_2}=\frac{3}{8}
\end{aligned}\)
For the organ pipe closed at one end.
First overtone \((n=3)\), .
For organ pipe open at both ends,
Third overtone \((n=4)\),
From (1) and (2)
\(\begin{aligned}
& \frac{3 v}{4 l_1}=\frac{4 v}{2 l_2} \\
& \Rightarrow \frac{l_1}{l_2}=\frac{3}{8}
\end{aligned}\)
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