Why are the pipes on a church organ all different lengths?

Answer 1

The differing lengths of pipes are what allow the organ to produce different pitches. Pitch (frequency) is directly related to pipe length. The longer the pipe the lower the pitch. This gives rise to the standard organ terminology that tells the performer at what pitch level a stop (or set of pipes) will sound. This is determined by the theoretical length of the lowest pipe in a particular stop. An 8-foot stop produces notes of unison pitch (on the manual keyboards - 16' for the pedal keyboard). A 4-foot stop produces pitches an octave higher than unison. A 2-foot stop is 2 octaves above unison. A 16-foot stop is one octave below unison, etc.

Answer 2

No. Of course not. In fact, to make them so, is virtually impossible. The width of any given organ pipe is determined by the scale and the halving ratio. The higher the note, the shorter the pipe and therefore the narrower the pipe. Your average small to medium sized church organ will have as it's largest pipe the low C of the 16" Bourdon which will be about 8 feet tall and 10 inches wide. The smallest pipe of, for instance, a 1 1/3' Larigot will be the size of a pencil. You can see why that pipe could not possibly be 10 inches wide to produce the proper pitch - it's usually about 1/4 inch wide. Pipes with a narrow width (compared to it's height) produce more harmonics (string pipes such as a Viola da Gamba) and wider pipes produce few harmonics (flutes, such as a Tibia Clausa) all things being equal.