A small hollow tube is glued to a speaker in a vertical manner. The speaker is set to play a single tone such that it vibrates vertically with simple harmonic motion. The speaker operates with constant amplitude, A, but variable frequency, f. A slender pencil is placed inside the tube.
A) At low frequencies the pencil stays in contact with the speaker at all times; at higher frequencies the pencil begins to rattle. Explain the reason for this behavior.
B) Find an expression for the frequency at which rattling begins.