MHT CET · Physics · Waves and Sound
The fundamental frequency of open pipe is 'n'. If it is closed from one end then frequency of the \(2^{\text {nd }}\) harmonic of closed pipe is higher by \(200 \mathrm{~Hz}\) than \({ }^{\prime} \mathrm{n}^{\prime}\). The value of 'n' is
- A \(800 \mathrm{~Hz}\)
- B \(200 \mathrm{~Hz}\)
- C \(100 \mathrm{~Hz}\)
- D \(400 \mathrm{~Hz}\)
Answer & Solution
Correct Answer
(D) \(400 \mathrm{~Hz}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{n}=\frac{\mathrm{v}}{2 \ell}\)
\(2^{\mathrm{nd}}\) harmonic \(=1^{\mathrm{st}}\) overtone \(=(2 \mathrm{p}+1) \mathrm{n}_{0}=3 \mathrm{n}_{0}\)
\(\frac{3 \mathrm{v}}{4 \ell}-\frac{\mathrm{v}}{2 \ell}=200\)
\(\frac{v}{2 \ell}\left(\frac{3}{2}-1\right)=200\)
\(\frac{v}{2 \ell}=400\)
\(2^{\mathrm{nd}}\) harmonic \(=1^{\mathrm{st}}\) overtone \(=(2 \mathrm{p}+1) \mathrm{n}_{0}=3 \mathrm{n}_{0}\)
\(\frac{3 \mathrm{v}}{4 \ell}-\frac{\mathrm{v}}{2 \ell}=200\)
\(\frac{v}{2 \ell}\left(\frac{3}{2}-1\right)=200\)
\(\frac{v}{2 \ell}=400\)
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