Final answer:
Theories that explain VF vibration include classical mechanics' concepts of forced oscillations and resonance, while the obsolete ether theory has been supplanted by field theory. Resonance happens at a system's natural frequency, which is related to the size of the resonating body and explains the absence of low-frequency resonance in shorter tubes.
Step-by-step explanation:
The theories that explain vibrational frequency (VF) include classical mechanics and quantum mechanics. Classical mechanics explains vibration through forced oscillations and the concept of resonance. The equations of motion associated with forced oscillations can predict how a system will respond to external forces. When a system is exposed to a periodic force at its natural frequency, it may enter a state of resonance, where the amplitude of oscillation reaches a maximum. This is due to the constructive interference of the waves produced by the force with the natural vibrations of the system.
Historically, the ether theory was believed to explain vibrations, suggesting that a non-physical medium was responsible for the propagation of waves and vibrations; however, this theory has since been disproven and replaced by field theory. Field theory describes how forces like gravity and electromagnetism can exert influence without direct contact, and it operates at the speed of light as was confirmed by twentieth-century experiments.
The absence of low frequencies at which both tubes resonate can be explained by the fact that longer wavelengths associated with low frequencies cannot fit into shorter tubes, and therefore, cannot establish standing waves which facilitate resonance. On the other hand, high frequencies with shorter wavelengths can resonate in both short and long tubes.