String Instrument as Model of Blackbody Radiation 2

Connecting to an earlier post we consider, as a model of radiation from a gas, a string instrument consisting of a vibrating string spanned over bridges on a soundboard with

• soundboard = radiating gas
• forcing of soundboard by vibrating string through bridges  = incoming radiation
• sound waves generated by vibrating soundboard   = outgoing radiation.

A string instrument has the following properties illustrating basic aspects of radiation from a gas:   

1. string is plucked into vibration 
2. string vibration over a sequence of frequencies (harmonics) = incoming radiation 
3. soundboard vibration in resonance with string vibration through bridges
4. soundboard vibration generates sound waves in surrounding air = outgoing radiation. 

We note in particular the following aspects of the soundboard = radiating gas:

• passive: when picking up the string vibration by resonance = incoming radiation
• active: when generating sound waves = outgoing radiation. 

Together gives the soundboard the role of passive mediator of string vibrations into sound waves, for selected frequencies. The flow of energy is from string to soundboard to surrounding air, without "backradiation" with the soundboard feeding energy into to string. 

A radiating gas of low temperature like the atmosphere has a similar passive function of transferring heat energy by infrared radiation from the Earth surface into outer space, for selected resonance frequencies of "greenhouse gases". The heat transfer is one-way from a warm Earth surface into outer space passively mediated by atmospheric "greenhouse gases", without "backradiation" from cold atmosphere to warm Earth surface.

Recall that CO2 alarmism is based on downwelling longwave radiation DLR as "backradiation" from the atmosphere to the Earth surface, measured by special DLR-meters fabricated according to a formula defining DLR in terms of temperature. But the formula is non-physical and the measured DLR has no physical reality.

The above discussion describes a periodic state with the string continuously being fed energy so that a sustained sound is generated. The dynamics of the model includes momentary input of energy into the string by plucking followed by transfer of energy from the string into the soundboard followed by transfer of energy into sound waves. The analog dynamics of radiation can be described as follows:

• start-up with the string and soundboard at rest: Earth surface and atmosphere at 0 K 
• plucking of string: Earth surface is heated (during daytime by the Sun) 
• vibrating string makes soundboard vibrate by resonance: Earth surface heats atmosphere by radiation 
• vibrating soundboard generates sound waves: atmosphere radiates to outer space 
• string loses energy without renewed plucking = Earth surface is cooling during night. 

A good instrument is made so that the string energy is transferred into the soundboard at rate giving the plucked note a sustain of proper duration, which is in principle controled by the masses of the string and soundboard, the tension of the string and the stiffness of the soundboard.