The flute is typically about 26 inches long and as we have seen this week it is an open tube at both ends. There are holes which are closed or opened by fingering valves that change its effective length, and the pattern and mechanisms to do this set various designs of flutes played now and in the past. Assume that the velocity of sound in warm moist air is 340 m/s. 1. Show that the resonant frequency of the flute without any open holes is close to middle C. Middle C is sometimes called "C4" and its frequency on the evenly tempered scale where A is 440 Hz is 261 Hz. 2. A flute finger hole is opened to force a node close to the point under the hole (actually, a little farther out). This has the effect of shortening the tube. Explain why this increases the frequency. 3. A flute player can also create higher frequencies by generating harmonics of the fundamental. With no holes open, by blowing harder on it, vibrations with shorter wavelengths will resonate in the tube. Again, thinking of the physics as a tube open at both ends without open holes otherwise, the fundamental has