Resonators are thin-walled tubes, typically made of aluminum, but any suitably strong material will do. They are open at one end and closed at the other. Each bar is paired with a resonator whose diameter is slightly wider than the width of the bar, and whose length to the closure is one-quarter of the wavelength of the fundamental frequency of the bar. The resonator for A3 (the lowest A on a vibraphone) is approximately 15 inches long. When the bar and resonator are properly in tune with each other, the vibrating air beneath the bar travels down the resonator and is reflected off the closure at the bottom, then returns back to the top and is reflected back by the bar, over and over, creating a much stronger standing wave and amplifying the fundamental frequency. The resonators, beside raising the upper end of the vibraphone's dynamic range, also affect the overall tone of the vibraphone, since they amplify the fundamental, but not the upper partials. There is a trade-off between the amplifying effect of the resonators and the length of sustain of a ringing bar. Basically, all of the energy in a ringing bar comes from the initial mallet strike, and that energy can go to making the bar ring either louder initially, or not as loud but longer. This is not an issue with marimbas and xylophones, where the natural sustain time of the wooden bars is short, but vibraphone bars can ring for many seconds after being struck, and this effect is highly desirable in many circumstances. Therefore the resonators in a vibraphone are usually tuned to be slightly off-pitch to create a balance between loudness and sustain.
Although I am not an expert in acoustics, what the writer discusses makes sense to me. This is not electronic amplification as in a conventional amplifier for sound reproduction or recording. In sound reproduction systems, we have a transducer (microphone, transforms acoustic energy into electic energy), an amplifier (a bunch of electronic omponents that amplify the electric signal coming from the microphone), and a speaker (transforms electric energy from the amplifier back into acoustic energy). In electronic amplifiers additional energy is provided from the electric power used to run the amplifier. In the resonator of a vibraphone there is no additional energy imparted: all the energy comes from the mechanical energy imparted to the metal bar by hitting it with the mallet. What the resonator does, as I understand what the article tells us, is channel the acoustic energy produced by hitting the metal bar with the mallet into the fundamental frequency of the sound wave. If there are any physics experts out there, please check and correct as necessary.
Another interesting discussion in this article refers to vibrato and tremolo.
Another difference in vibraphone resonators is the presence of a rotating disk at the top of each resonator. The disks for a group of resonators are ganged together with a shaft that can be driven from an electric motor to cause the disks to rotate. When the disks are open (standing vertically) the resonators have full function. When the disks are closed (lying horizontally) the vibrating column of air is blocked, reducing the amplification effect. As the disks rotate, this varies the amplitude of the instrument, creating a "vibrato" effect. Some argue that calling this effect vibrato is incorrect, saying that vibrato is a variation in pitch, not amplitude. The correct term should be tremolo, a variation in amplitude, and therefore the vibraphone is incorrectly named; it should be called a tremolophone. Others argue that the common usage of vibrato and tremolo is nowhere near that precise, even among experienced musicians who should presumably know better. Additionally, in this context, there is the extra consideration that the rotating plates interfere with wave-fronts in the resonator tubes to cause doppler-effect pitch variations. This can be observed using an oscilloscope.
Tremolophone, vibraharp, harpophone, harpaphone, telephone, vibraphone -lots of interesting words. The music business is full of nice words, radiola, motorola, electrola, claxtonola, etc.