A vertical hollow tube is connected to a speaker, which vibrates vertically with simple ha...

A vertical hollow tube is connected to a speaker, which vibrates vertically with simple harmonic motion (Figure). 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.

FIGURE