(a) The fundamental in a open–open pipe looks like this and is ½ of a wavelength of the wave. Since this ½ wavelength fits in the length L, the total wavelength would have to be 2L.
![](https://www.sarthaks.com/?qa=blob&qa_blobid=10793240469181596937)
(b) Simply use v = f λ → v = 2Lfo
(c) Harmonics are multiples of the fundamental, so the next frequency is 2fo
(d) This is the same tuning fork so it is the same wavelength and waveform but the bottom is now closed so the wave looks like this.
![](https://www.sarthaks.com/?qa=blob&qa_blobid=12145309679981094158)
The tube we had initially, fit ½ of a wavelength inside, and since its the same wavelength wave, again ½ of the wavelength of this wave would fit in length L and it would look like this.
![](https://www.sarthaks.com/?qa=blob&qa_blobid=13600782755978417876)
This is impossible for a standing wave in an open–closed tube, and its also not the fundamental anyway so we have to change the length to make it look like the fundamental, Shown below. To do this, we make the length half of what it used to be.
![](https://www.sarthaks.com/?qa=blob&qa_blobid=10898699948569965395)