MHT CET · Physics · Waves and Sound
On closing an open organ pipe from one end, it is noticed that the frequency of third harmonic is \(50 \mathrm{~Hz}\) more than the fundamental frequency of vibration in open organ pipe. The fundamental frequency of open organ pipe is
- A \(250 \mathrm{~Hz}\)
- B \(100 \mathrm{~Hz}\)
- C \(50 \mathrm{~Hz}\)
- D \(200 \mathrm{~Hz}\)
Answer & Solution
Correct Answer
(B) \(100 \mathrm{~Hz}\)
Step-by-step Solution
Detailed explanation
Fundamental frequency of closed pipe \(=\mathrm{n}_{1}=\frac{\mathrm{V}}{4 \ell}\)
Frequency of third harmonic \(n_{3}=\frac{3 \mathrm{~V}}{4 \ell}\)
Fundamental frequency of open pipe \(=n_{1}{ }^{\prime}=\frac{V}{2 \ell}\)
\(\frac{3 \mathrm{~V}}{4 \ell}-\frac{\mathrm{V}}{2 \ell}=50\)
\(\therefore \frac{V}{4 \ell}=50 \quad \therefore \frac{V}{2 \ell}=100 \mathrm{~Hz}\)
Frequency of third harmonic \(n_{3}=\frac{3 \mathrm{~V}}{4 \ell}\)
Fundamental frequency of open pipe \(=n_{1}{ }^{\prime}=\frac{V}{2 \ell}\)
\(\frac{3 \mathrm{~V}}{4 \ell}-\frac{\mathrm{V}}{2 \ell}=50\)
\(\therefore \frac{V}{4 \ell}=50 \quad \therefore \frac{V}{2 \ell}=100 \mathrm{~Hz}\)
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