Well, allow me to have a go at this, please. Correct me if incorrect. Simplistic...
The question is: do I need more air for a larger bore? The answer: it depends.
Why: Boyle’s Principle. Pressure and volume have an inverse function. If volume increases, pressure decreases.
Why is this relevant? Our ears. Our ears respond to 2 factors only: pressure and vibration. Our ears transform pressure and vibration into a signal to our brain, and our brain interprets this signal as sound.
So, to produce a sound from a trumpet, we need pressure and vibration. So how to do?
First, some basics.
- A trumpet is filled with ambient air, and air has mass, and thus the ambient air will have an inertial resistance to change.
- To produce a sound, that air must be disturbed; i.e perturbed, which results in perturbations.
- When the perturbations repeat consistently in cycles over a unit of time, they become vibrations, and we call this a frequency.
- When we increase the pressure of the perturbations within the trumpet, we increase the potential energy of those perturbations; and when that energy is released at the end of the trumpet (the bell), we hear this release of increased pressure as an increase in amplitude (loud).
- No frequency, no sound. The source and means of frequency is our lips.
- No pressure, no sound. The source and means of pressure is the air from our lungs applied to the ambient air inside the trumpet.
Q1. So, do WE need air to make a sound?
A1. YES. Why? The air we push out from our lungs vibrates our lips. No air across our lips, no vibration. Try vibrating your lips without blowing air through them.
Q2. Does the trumpet need extra air to make a sound?
A2. NO. Why? The trumpet is already filled with ambient air. It needs a perturbation and a pressure to get that air to vibrate and produce the sound we hear.
Q3. So why do we see almost no air flowing out of the horn, when we use the smoke method? After all, when we ‘blow’ into the mouthpiece, we feel the release of air from the mouthpiece (m/p). Why is the bell output different from the m/p input (ie why the smoke test shows near zero air flow)?
A3. The key is Volume.
(a) First, we need to know exactly what occurs when air is vibrated at a specific frequency.
A wave is created, having nodes and antinodes. Textbooks illustrate this as a 'sine wave'; but this is incorrect, actually. Both the sine and cosine waves should be shown graphically, sort of like this … ∞∞∞ (I am trying to keep the physics to a minimum).
Why is this important? Because this is how the wave forms inside the trumpet, what exits, and what you hear. What we hear is the antinode, because this is the amplitude: the node has zero amplitude, but maximum pressure. The node must form at the bell: thus the bell shape and volume are critical for sound.
(b) If you blow directly into the lead pipe, you will feel air flow out of the bell (but no pitch). But the outflow will very be very much slower than what you inflow, and it will have much less force (pressure). The reason is simple; volume. As volume increases, pressure must decrease. If the outflow point has a much greater area than the inflow point, the flow from input to output will be very much reduced. The analogy is using a garden hose to fill an outdoor pool. Only a very small volume of water can be pumped through a garden hose, but with high pressure the flow velocity can be very high. If a small volume container is filled, the fill rate is rapid. But try to fill a pool, and the fill rate is very slow. The reason is volume. To prevent overflow, the pool may have an exit port. If the exit port is very much larger in area than the hose nozzle, the flow and pressure of water exiting the pool will be very slow and very low.
(c) So with Volume, Pressure, Velocity, Frequency, we can now comprehend our trumpet and our interaction.
(i) We fill the m/p with a volume of air, moving at some velocity, and vibrating at some frequency. The m/p exit hole is about 3mm. The cup width/depth varies greatly, but let’s peg at 16mm x 8mm. If the bowl is semi-spherical, the max volume will be 2.15ml. The air exiting the m/p will have a noticeable pressure and velocity.
(ii) As our air flows through the trumpet, it must flow through an ever increasing volume. Two results: the pressure decreases; and the wave from the m/p elongates and drops in frequency. If the exit diameter at the bell is 70mm, this alone will account for a reduction of over 20x the input pressure. When we consider the volume of the horn to the m/p volume, the scale factor is huge. Thus the combined factors result in a very low volume and low pressure of air exiting the horn: the resulting air flow may be <1% of the input. Thus we perceive almost zero effects for the smoke test.
Q4. So what about sound volume? Why must I blow harder to get more sound volume? Notice: we are talking about “sound volume” (ie Amplitude) exiting the horn, not physical “air volume”.
A4. Pressure. (physics: the node is point of maximum pressure, thus the antinode is the least pressure). Amplitude is the antinode. Thus for a max antinode, we must have a max node (pressure). We create pressure by blowing air into a vessel (m/p) that is less in volume than the feedstock volume (our lungs). The more pressure we create, the more resulting amplitude.
Q5. Ok. But what about the high notes? Why do these require more effort than the lower notes?
A5. 2 reasons.
(i) Our bodies are very limited in capacity. Our lips are extremely limited and weak: in “natural” state, they are simply not engineered to vibrate at high tension to create high frequency vibrations. We must train our lips/embouchure into a very unnatural state. This requires effort to develop and to apply on demand.
(ii) High notes result from high frequencies exiting the horn. A high frequency requires many times more nodes than a low frequency. Nodes result from pressure. Thus as frequency increases, we must apply more air pressure to create the nodes AND we must increase the tension in our embouchure. The combined factors result in an exponential function: ever increasing tension and pressure.
Q6. Bore. How does the bore of the trumpet factor into all this?
A6. Complicated. The bore relates to the diameter of the tubing at valve #2. In theory, a larger diameter tube will have volume greater than a smaller diameter. But this does not mean a trumpet of L bore will have an overall volume greater than one of ML bore: the bell shape and length is a significant factor to overall volume, and thus an L bore horn can be equal in overall volume to an ML bore horn, and vice versa. Added to this, is the internal resistance of each horn, which is in itself a very complicated aspect to analyse: lead pipe taper; thickness of tubes; radius of bends; bell taper and flare; and more are all factors. Added to this is “dual bore”, where the connection to the bell is usually larger than the rated bore: which creates a lower pressure point within the horn, and presumably this results in lesser internal resistance.
So does a larger bore horn require more air? The honest answer is “it depends”.
I hope this long winded post has not bored too many people.
