Answer
At the midpoint. Two pieces.
Work Step by Step
It is very important to look at Figure 21.5 when answering this question.
If a string vibrates in two segments, as shown in the second diagram in Figure 21.5, a tiny piece of paper can be supported at the midpoint, because there is a node there and the paper won't be thrown off by oscillations.
If a string vibrates in three segments, as shown in the third diagram in Figure 21.5, two pieces of paper can be supported on the string, at points that are one-third and two-thirds of the way along the string (i.e., equally spaced from the endpoints and from each other).
In general, if a string vibrates in n segments, (n-1) pieces of paper can be supported on the string, at points that are equally spaced from the endpoints and from each other.
