(11) [8 points] You have a long pipe, length L, that is closed at both ends. The pipe is filled with a gas with speed of sound 12. The pipe is excited in order to produce standing sound waves. (a) Sketch the standing wave pattern of air displacement for the four lowest frequencies supported by this pipe. Label the displacement nodes and antinodes. (b) Make a table of the wavelengths and frequencies of the sound waves that are formed by these four excitations, in terms of L and v. (c) Find a general expression for the wavelength and frequency of the nth harmonic in terms of Aland f1, the wavelength and frequency of the fundamental excitation. (d) The tube is filled with propane and excited at 630 Hz (the harmonic number n is unrecorded but large enough that many nodes and antinodes are observed. The standing wave pattern is measured. The distance between nodes is equal to 21 cm. Find the speed of sound in propane. (e) A theoretical calculation for the speed of sound is given by equation 16.10 in your textbook. Propane has chemical composition C3H3 and a specific heat ratio (JP/CV of 1.13. Calculate the predicted speed of sound in propane at 300K