## Harmonics with Open/Closed end condtions - FFT analysis

If you blow air across the end of a tube, you can excite resonant harmonics. This is a very simplistic view of the frequency spectrum based on different end conditions for sound harmonics in a tube. (The length of the tube is assumed to be after any "end corrections" have been made.) See the equations here.

Initial conditions :    Length (L) (m) =          (0.2-2 m)      Velocity of Sound (V) (m/sec) =        (200-400 m/s)
Ends of the tube :        Ends OPEN          Ends CLOSED        Only one OPEN

Questions:
A) If you increase the LENGTH of the tube, what happens to the frequencies in the spectrum (do they shrink or grow) - and why? (Hint: Think of the wavelength fitting in the tube.)
B) If you increase the VELOCITY of the sound, what happens to the frequencies (do they shrink or grow) - and why? (Hint: If wavelength fixed, how would velocity change affect the frequency?)
C) How does opening one end affect the spectrum (compared to the both-open or both-closed)? How is the difference between frequencies related to the fundamental and why? How are they related for the both-open or both-closed?
D) Suppose you knew the velocity, what kinds of ends, and two adjacent frequencies ... can you figure out the length? (Hint: set up equations to represent each frequency with n1 and n2 as unknowns. What is the relationship between n1 and n2?)