Picture From You Can't Always Hear the Shape of a Drum by Barry Cipra
1) Compute the total perimeter of the first band on the top by adding the
perimeter of each piece. This represents the length of wood or metal that
wraps around the outside of the drums.
2) Compute the total perimeter of the second band.
3) Do both bands have the same total perimeter?
4) If we hit our drums too hard and broke through them, then we would have to replace the material that covers the drum heads. Compute the total area of the first band by adding the area of each piece.
5) Compute the total area of the second band.
6) Do both bands have the same total area?
7) What does it mean when we talk about the shape of a two piece band? Why do we say that the shape of the first band is different from the shape of the second band?
8) If we built drums that look just like the pictures, then we could play one of the bands by hitting both drums in that band at the same time. How would you test to see if the first band sounds the same as the second band?