The time-dependent frequency and energy of free vibration of the spagetti problem, that is the axially moving continuum with time-varying length, are investigated. Exact expressions for the natural frequency and time-varying vibration energy are derived by dealing with traveling waves. The vibration period increases with increasing length, but the free vibration energy decreases. When the string undergoes retraction, the vibration energy increases with time. The free response of the time-varying string is represented by superposing two traveling waves.