An organ pipe is made from a brass tube closed at one end as shown. The pipe is 3.4 meters long. When driven it produces a sound that is a mixture of the first, third and sixth harmonic (mode).
a) What are the frequencies of these modes?
b) Sketch the wave amplitudes for the third harmonic mode (only) in on the figure, indicating the nodes and antinodes. Be sure to indicate whether the nodes or antinodes are for pressure/density waves or displacement waves!
c) The temperature in the church where the organ plays varies by
around 30
C between summer and winter. By how much (approximately) does this vary the frequency of the fundamental
harmonic? (Indicate why your answer is what it is, don't just
put down a guess).