In my Physics textbook, it says that if two pendulums of the same natural frequency are placed next to each other and if one is set into vibration, the other starts resonating and when the first one gets damped due to air friction, the vibration of the second one again sets the first into vibration (resonance) and this goes on until all the energy is dissipated as sound. My Question is: If placed in vacuum, will these two complement each others' vibrations and continue vibrating in perpetual motion (because there isn't any propagation of sound in vacuum due to absence of a medium)?
[Physics] Resonance and natural vibrations in vacuum
acousticsfrequencyresonancevacuumvibrations
Related Solutions
For a vibration to exist, something has to vibrate. In the water vibrations it is water molecules. In light it is electric and magnetic fields that vibrate.
In gravitational waves it is the space itself that changes , (x,y,z,t) between points becomes larger and smaller and the wave is seen as a distortion of the ring of partilces, the image is of one wavelength passing.
The mainstream gravitational theory is General Relativity which assumes that what we called gravitational field is an effect on the space time fabric created by the presence energy and masses. The space itself is constructed by the existence of these. Gravitational waves arose from the solutions of the differential equations of general relativity for specific boundary conditions. The "medium" you are looking for is space time itself.
Yes, the room has a lot of air, but most of it isn't in direct contact with the vibrating string. In order for the string to make much sound, it needs to transfer some of its energy to the surrounding air, but there are a couple of issues which make that difficult.
Firstly, the string has a relatively small surface area, so it simply doesn't directly contact very much air.
Secondly, the string isn't very effective at transmitting its vibrations to the surrounding air. It's a bit like if you get a thin rod and wave it back and forth in water. Yes, it makes a few ripples, but the rod mostly just cuts through the water. But if you get a wide paddle and wave it around, then it's easy to make large waves in the water. Similarly, a vibrating string mostly just cuts through the air, rather than making useful pressure waves in it.
With air, it's even harder to effectively induce waves than in water, because it's so compressible. Obviously, pressure waves do travel through the air, but it's a lot harder to transmit such waves through a gas than through a denser, stiffer medium.
So stringed instruments generally have some kind of soundboard: a surface with a relatively large area that's in contact with a lot of air. The string can efficiently transmit its vibrations to the soundboard, and the soundboard can, in turn, transmit those vibrations to the air.
On a guitar, the soundboard is the front of the body. Here's a diagram, courtesy of Wikipedia:
The soundboard of a piano is inside the body:
(source)
An important concept here is acoustic impedance.
Acoustic impedance and specific acoustic impedance are measures of the opposition that a system presents to the acoustic flow resulting from an acoustic pressure applied to the system. [...] There is a close analogy with electrical impedance, which measures the opposition that a system presents to the electrical flow resulting from an electrical voltage applied to the system.
Unfortunately, that Wikipedia article is heavily technical and mathematical, without much physical detail.
The soundboard of a musical instrument, or the membrane of a loudspeaker, doesn't need to have a lot of back and forth movement. It just needs to vibrate relatively gently. Large movement wastes energy by causing bulk movement of the air, rather than inducing the desired pressure waves.
Best Answer
No, because in a vacuum, there is no way for the two tuning forks (I think you meant this, rather than pendulums) to communicate. The reason a second tuning fork with the same resonance frequency will begin resonating is because, physically, sound waves are hitting it at its natural frequency. Sound waves travel in a medium, so in a vacuum, there's nothing to carry the sound waves and, hence, no communication between the tuning forks.