Notes on Free Response Question 5 (Next Page)
In my opinion this is a flawed question.
The author meant for you to assume that both ends of the string
are Nodes.
This is not strictly true because the left end of the string is
being forced to vibrate. The up and down arrows on the diagram
clearly indicate vertical vibration at the left end of the
string.
However, the oscillator in a typical lab situation is of small
amplitude. In this case the oscillations at the left end of
the string are much smaller in amplitude than the oscillations
found at the antinodes between the ends of the string.
The author should have told you to approximate the left end of
the string as a Node.
Take both ends of the string as a Node in your solution. This
is actually an excellent approximation.