Questions

$(1)$ Suppose you find that in a similar experiment involving an open$-$closed tube, the n$=3$

resonance occurs at $369$ Hz $.$ At what frequency would you expect to find the next harmonic?

$(2)$ The pipes in organs are much bigger than our tube. What would be the fundamental

frequency of an organ pipe of length L$=2\mathrm{.}40$m and diameter D$=15\mathrm{.}5$cm$,$ which is open at

both ends? Assume a standard room temperature of $70\backslash$deg F$.$ Show you work.

$(3)$ In contrast, the length of a piccolo $($small flute$)$ is only $32\mathrm{.}0$ cm $.$ The resonating air column

vibrates as in a pipe that is open at both ends. Find the frequency of the lowest note that a

piccolo can play. Assume a standard room temperature of $20\backslash$deg C$.$ Show your work.