Search any question & find its solution
Question:
Answered & Verified by Expert
A closed organ pipe and an open organ pipe have their first overtones identical in
frequency. Their lengths are in the ratio
Options:
frequency. Their lengths are in the ratio
Solution:
1745 Upvotes
Verified Answer
The correct answer is:
$3: 4$
First overtone of a closed pipe is given by
$$
\mathrm{f}=\frac{3 \mathrm{~V}}{4 \ell}
$$
First overtone of an open pipe is given by
$$
\mathrm{f}^{\prime}=\frac{\mathrm{V}}{\ell^{\prime}}
$$
Since $\mathrm{f}=\mathrm{f}^{\prime}, \quad \frac{3 \mathrm{~V}}{4 \ell}=\frac{\mathrm{V}}{\ell^{\prime}}$
$$
\therefore \frac{\ell}{\ell^{\prime}}=\frac{3}{4}
$$
$$
\mathrm{f}=\frac{3 \mathrm{~V}}{4 \ell}
$$
First overtone of an open pipe is given by
$$
\mathrm{f}^{\prime}=\frac{\mathrm{V}}{\ell^{\prime}}
$$
Since $\mathrm{f}=\mathrm{f}^{\prime}, \quad \frac{3 \mathrm{~V}}{4 \ell}=\frac{\mathrm{V}}{\ell^{\prime}}$
$$
\therefore \frac{\ell}{\ell^{\prime}}=\frac{3}{4}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.