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

----- 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)

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