An organ pipe of length L open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of 480 Hz. What should be the length of a pipe closed at one end, so that it also vibrates in its first harmonic with the same tuning fork?

This is a short answer type question as classified in NCERT Exemplar

As the organ pipe is open at both ends, hence for first harmonic

l= $\frac{\lambda }{2}$

$\lambda =2l$

V=c/2l

For pipe closed at one end

V’=c/4L’

Hence v=v’

c/2L =c/4L’

L’/L=2/4=1/2

L’=L/2

<p><span data-teams="true">This is a short answer type question as classified in NCERT Exemplar</span></p><p>As the organ pipe is open at both ends, hence for first harmonic</p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745487959phpWxKNGG_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745487959phpWxKNGG.jpeg" alt="" width="203" height="118"></picture></div></div><p>l=<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>λ</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> </math> </span></p><p><span contenteditable="false"> <math> <mi>λ</mi> <mo>=</mo> <mn>2</mn> <mi>l</mi> </math> </span></p><p>V=c/2l</p><p>For pipe closed at one end</p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745487990phpLzeV7Y_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745487990phpLzeV7Y.jpeg" alt="" width="195" height="93"></picture></div></div><p>V’=c/4L’</p><p>Hence v=v’</p><p>c/2L =c/4L’</p><p>L’/L=2/4=1/2</p><p>L’=L/2</p>

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