Re: Re: Subject: Re: [Harp-L] comb material

["Vern Smith" <jevern@xxxxxxx>]

----- Original Message ----- 
From: "Garry Hodgson" <garry@xxxxxxxxxxxx>
To: <harp-l@xxxxxxxxxx>
Sent: Thursday, April 19, 2007 9:57 AM
Subject: Re: Re: Subject: Re: [Harp-L] comb material


>  it was my understanding, probably from something i read
> here, that harps make sound not by vibrating reeds, but by chopping
> up the airstream in similar fashion to a siren.  this is why the music
> box analogy has problems, since the sound generation mechanism
> is so different.

There are several things happening at once.

1. The air flowing through the gap and across the under side of the reed 
generates a downward "lift" and causes the reed to move down.  This is the 
bernoulli effect like the flow of air over an airplane wing.
2. When the reed enters the slot, the airflow is cut off and the downward 
force ceases abruptly.
3. The reed's momentum carries it to the end of its downward movement, 
bending down as a leaf spring.
4. The restoring spring force in the reed causes the reed to rise again, 
exiting the slot.
5. The  momentum carries the reed to the end of its upward movement, bending 
the reed up as a spring.
6. As the gap opens, the air flows again, the downward bernoulli force 
occurs again, and the cycle repeats.
7. The pitch is proportional to the square root of the spring constant of 
the reed divided by the mass of the tip.  f = 2*pi* sqrt( k / m). In other 
words, making the reed stiffer increases the pitch and making the tip more 
massive lowers it.  We all knew that already!   ;o)   The square root means 
that we have to increase the mass of the tip or lower the spring stiffness, 
or lower their ratio by a factor of four to lower the pitch one octave...and 
vice versa..

The reed is a mechanical oscillator.  In an oscillator, there must be a 
variable force applied to the elastic element that is about 90 degrees out 
of phase with the displacement.  The harmonica reed meets these requirements 
and as we all know, vibrates.   Energy from the airstream makes up for the 
drag of the tip "waving in the breeze"  When you quit blowing, these losses 
gradually drain the energy stored in the spring/reed and the vibration 
dies..

The motion alternately allows and shuts off air flow through the gap and 
slot, "chopping" the airstream.  This varies the pressure in the vicinity of 
the reed and generates the characteristic harmonica siren sound. It is so 
much louder, that the low-level "music-box" sound emanating directly from 
the reed is masked to the human ear.  The movement of the sound is mostly 
independent of the motion of your breath through the harp.  Consider how 
little difference there is between the sounds of  blown and drawn reeds. 
The sound travels through the air at about 1100 ft/sec and your breath 
travels through the harp at less than a tenth of that.

Although the motion of the reed is sinusoidal,  the flow area between the 
reed and slot varies in a is very non-linear manner, e.g. it shuts off 
abruptly just as the reed enters the slot.  This non-linear variation 
generates very strong, mostly odd, overtones.  It accounts for the rich, 
raspy, square-wave-like timbre of the harmonica reed.

Understanding how the sound is generated, it is easy to understand that any 
reed of the same pitch that you blow at the same pressure will have the same 
harmonica sound.

As you blow harder, the pitch will decrease slightly.  This effect is 
greatest for low-pitched reeds and almost disappears at the highest pitches. 
I don't know why.

> am i misunderstanding?  can someone clarify?
I hope that the above is a clarification and not an obfuscation.   ;o)

Vern
Visit my harmonica website www.Hands-Free-Chromatic.7p.com