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From: WVE~ol.com
Date: Fri, 13 Feb 1998 15:27:17 EST
Subject: back pressure

In a message dated 98-02-13 04:20:57 EST, Douglas T. writes:
> I feel 'back pressure' ...
> But... the reason for me to feel it is the way in which I start my notes
> and the attack I put on some notes... It is this crucial few thousandths
> of a second which is where the 'feel' comes from
(snip)
> What is happening is that the initial wave front pressure is ... I think
> ... many times as powerful as the steady state 'push' of air. This
> being so the differential in pressure in the mouthpiece and the chamber .
> before 'getting to the reed' is what gives me the feeling of restriction.

I accept your concession that the hole size makes no perceptible difference in
back pressure during steady-state playing. Now you raise a new claim that the
differences among chromatic hole sizes affect the response of the harps to
transients...attacks and releases.

It takes 9 microseconds for a pressure disturbance to travel the length of the
reed chanber at 1100 ft/sec, the velocity of sound. This means that whatever
the pressure in the chamber is, it is essentially the same throughout.

However, it might take longer to raise the pressure of the chamber if the flow
into the chamber is restricted. Your point seems to be that the flow
restriction of the hole entrance combined with the volume of the reed chamber
delays the effect of pressure transients (attacks and releases) on the reed.
I am sure that the effect exists at some level. The following analysis is
needed to quantify the effect:

Consider the volume of the reed chamber = 1.16" * .32" * .215" = .08 cubic
inches in a CX12.

Now assume the chamber is at atmospheric pressure and you instantly apply 10
inches of water pressure (about three times normal playing pressure) at the
hole entrance. Two questions arise:

1. How much volume of air must flow into the chamber to raise its pressure
to equal the pressure in your mouth?
2. How much time will be required to supply that volume of air at flow rates
that you normally supply with your breath?

The added volume is dV = V1 * (P2/P1 -1 ) = .08 * (417 / 407 -1 ) = .002
cu. in.
Note that atmospheric pressure is about 407 inches of water. If your lung
exhales about 20 cubic inches per breath (from Taber's Medical Dictionary)
then the added volume to raise the chamber pressure will require .002 / 20
=.0001 or only one ten-thousandth of a normal breath! This sudden requirement
for a tiny amount of extra air is not perceptable to the player.

I have measured the airflow required to sound a reed at full volume in the
range of 5 to 15 cubic inches per second. Let us be very conservative and
assume that you can only supply 5 cu. in. per sec. The pressure will rise in
about .002 / 5 = .0004 seconds or 0.4 milliseconds. Now consider that at a
constant pressure, the flow through the mouthpiece hole will be proportional
to the area. That means that the time to raise the pressure in the 270
chamber = ( Acx12 / A270 ) * cx12time (.048 / .031 ) * .0004 = .0006 seconds or 0.6 milliseconds.

It only takes 0.2 milliseconds longer to raise the pressure in the 270 chamber
than it does to raise the pressure in the CX12 chamber. That isn't enough
time for you to perceive the difference. Nerve impulses don't travel fast
enough. Not only that but you cannot change the pressure in your mouth in 0.2
milliseconds.

Because the period of the C4 reed is about 4 milliseconds, it isn't going to
respond differently to pressure changes that are different by only 0.2
milliseconds.

The above numbers could be off by a couple orders of magnitude and still
support my point that the time constant of the hole-and-chamber has a
negligible effect on attack/decay pressure transients.

We could also compute the frequency of the hole-and-chamber as a Helmholtz
resonator to get an idea of its time constant. I'll give you a break and
leave that to another post.

Vern



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