Final answer:
The distance of resonance in a tube closed at one end represents one-fourth of a full wavelength for the fundamental frequency, and three-fourths for the first overtone.
Step-by-step explanation:
When the sound starts to resonate from a tube at a certain spot, the distance from the closed end where there is a node, to the open end where there is an antinode, represents one-fourth of a full wavelength. Therefore, the length of the tube (L) is equal to one-fourth the wavelength of the standing wave, hence λ = 4L. This fundamental mode of vibration is the natural frequency of the air column within the tube. Higher-frequency sounds, known as overtones, can resonate at shorter wavelengths. For example, when the tube resonates in such a way that three-fourths of a full wavelength fits within the tube length, this means L = (3/4)λ, and thus λ is equal to (4/3)L.