[Harp-L] Re: Reed Stress and Temperature

[patpowers <patpowers@xxxxxxx>]

Thanks Vern, very good explanation.  I did a little research on Young's Modulous and you are 100% correct, the elasticity of brass actually increases at lower temperature. ..go figure!  Thanks for the education - I guess I won't be wasting time warming up my harps to breath temperature any more.

Thanks, and Keep Harpin'!
Pat Powers



----- Original Message -----
From: "Vern" <jevern@xxxxxxx>
To: "patpowers" <patpowers@xxxxxxx>
Cc: "Larry Sandy" <slyou65@xxxxxxxxx>, harp-l@xxxxxxxxxx
Sent: Wednesday, September 24, 2014 1:23:27 AM
Subject: Re: Reed Stress and Temperature


On Sep 23, 2014, at 3:52 PM, patpowers <patpowers@xxxxxxx> wrote:

> Thanks Vern - I love a good debate! ;)
> 
> ââ.., but my point is all materials get stiffer, and lose elasticity, as temperature decreases.

They gain elasticity (the value of E goes up) as the temperature decreases.

> And, I wouldn't necessary dismiss a 50ÂF to 80ÂF change in temperature as negligible.

I didnât say that a 30 degF temperature change is negligible but that the effect on pitch is negligible.

>  On the flip side, I wouldn't consider brass to be brittle at 50ÂF either, but it is less elastic than brass at 80ÂF, especially when stressed and already fatigued.

As above, it is more elastic (higher value of E) at lower temperature.  i.e the restoring force is greater with equal deflection.
> 
> Regarding your statement "Reed behavior that concerns us takes place within the elastic zone below the yield point."  If this were entirely true, then reeds would never fail.

Reeds can fatigue and fail without ever being cycled at stresses as high as the yield point.  The yield point is that stress that will produce a permanent deformation. You exceed the yield point when you change the gap.

>  Obviously the elasticity eventually diminishes to the point where the behavior exceeds the yield point.

The elasticity ( value of E) is a property of the metal and does  not change with time.  When a reed fails in fatigue it cracks and that is what changes the stiffness and causes it to go flat..
  
>  At some point the metal fatigues and fails, and I still say colder temperature will accelerate this process.
> 
> Your argument is based upon the postulate that amplitude is the only stress factor effecting the reed.  You're not acknowledging temperature effect, or the effect frequency (omega) has on a vibrating mechanical system.

Displacement from its position of rest is the only thing that can cause stress in a reed.  Because it is free to expand, changes in temperature do not cause stress in a reed. Because it is fixed at both ends, temperature expansion/contraction can cause stress in a guitar string.

>  It is well known that harmonic frequencies can prove catastrophic to any mechanical system that vibrates.  I will exaggerate again to make my point, and use the example of Ella Fitzgerald shattering a wine glass with her voice.  It's not just the amplitude of her voice, but also the frequency (actually a harmonic frequency) matching the resonant frequency of the object.  I understand that glass is much more brittle than brass by orders of magnitude, but my point is all materials have resonant frequencies, and breaking points, and as frequency increases, so does the root mean power (amplitude/time) of the system.  You can't just ignore the effect frequency and temperature have on a mechanically vibrating system.  I agree that amplitude may be the primary contributing factor, but it is not the only contributing factor. 

The resonant factors you mention result in excessive amplitude and that is what does the damage.  In a system with low damping, matching the excitation to the resonant frequency can result in excessive amplitude.  As the damping (loss of energy per cycle) approaches zero, the amplitude and stress approach infinity.  As you approach the resonant frequency of a glass, the increased amplitude makes the straw dance before the glass breaks..  
> 
> High frequencies and harmonic distortion can be extremely damaging. Everyone knows that harmonicas give off harmonic frequencies, hence the instrument being called a "harmonica", and many of those frequencies are well above the hearing range of the human ear.  It;s not the amplitude of a harmonica that hurts a dogs, it;s the high frequncies.  Those high frequencies can also accelerate metal fatigue, and bending notes creates a huge amount of harmonic distortion, especially during the the transitional phase, which can be catastrophic.

> When sweeping a frequency that give off high harmonics, you'll eventually hit a frequency that matches the harmonic frequency of the material.

Resonance is not a property of the material.  A resonant mechanical system requires a spring acting on a weight. The strength of the spring and the mass of the weight determine the resonant frequency. Stronger springs and smaller weights tend to produce higher resonant frequencies.

The reed does not vibrate at those higher overtones.  They are caused by the non-linearities of air flow as the reed passes through the slot.  Jim Antaki has experimented with sensing reed position optically.  He has confirmed that the high overtones are absent from the signal from the sensors.  He uses an audio effects processor to restore the characteristic sound of the harmonica.

Vern