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A pipe, 30.0 cm long. Is open at both ends. Which harmonic mode of the pipe resonates a 1.1 kHz source? Will resonance with the same source be observed if one end of the pipe is closed ? Take the speed of sound in air as 330 m s^(-1).

Answer» <html><body><p></p>Solution :The first <a href="https://interviewquestions.tuteehub.com/tag/harmonic-1015999" style="font-weight:bold;" target="_blank" title="Click to know more about HARMONIC">HARMONIC</a> frequency is given by <br/> `v_(1) = (v)/(lamda_(1)) = (v)/(2L)` (open pipe) <br/> where L is the length of the pipe. The frequency of its nth harmonic is: <br/> `v_(n) = (nv)/(2L)`, for n = 1,2,3. ……….(open pipe) <br/> First few modes of an open pipe are shown in Fig. 15.15. <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/NCERT_BEN_PHY_XI_P2_C15_SLV_005_S01.png" width="80%"/> <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/NCERT_BEN_PHY_XI_P2_C15_SLV_005_S02.png" width="80%"/> <br/> For L = 30.0 cm, `v = 330 m s^(-1)`, <br/> `v_(n) = (n 330 (m s^(-1)))/(0.6 (m)) = 550 n s^(-1)` <br/> Clearly , a source of frequency 1.1 kHz will resonate at `v_(2)`, i.e. the second harmonic. <br/> Now if one of the pipe is closed (Fig. 151.15). <br/> it <a href="https://interviewquestions.tuteehub.com/tag/follows-994526" style="font-weight:bold;" target="_blank" title="Click to know more about FOLLOWS">FOLLOWS</a> from Eq. (14.50) that the fundamental frequency is <br/> `v_(1) = (v)/(lamda_(1)) = (v)/(4L)` (pipe closed at one <a href="https://interviewquestions.tuteehub.com/tag/end-971042" style="font-weight:bold;" target="_blank" title="Click to know more about END">END</a>) <br/> and only the <a href="https://interviewquestions.tuteehub.com/tag/odd-584820" style="font-weight:bold;" target="_blank" title="Click to know more about ODD">ODD</a> numnbered harmonics are present : <br/> `v_(3) = (3v)/(4L), v_(<a href="https://interviewquestions.tuteehub.com/tag/5-319454" style="font-weight:bold;" target="_blank" title="Click to know more about 5">5</a>) = (5v)/(4L)`, and so on. <br/> For L = 30 cm and `v = 330 ms^(-1)`, the fundamental frequency of the pipe closed at one end is 275 Hz and the source frequency corresponds to its fourth harmonic. Since this harmonic is not a possible mode, no resonance will be observed with the source, the moment one end is closed.</body></html>


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