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Reduce the impedance mismatch
- In general, a rapidly flaring bell is added to the end of the instrument to reduce the impedance mismatch as the sound emerges from the instrument, thus increasing the ability of the instrument to radiate sound.
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Oct 28, 2008 · A flared bell is why a trumpet makes a pretty tone instead of sounding like a gas pipe. The flare actually is percieved by the flow as resistance to the forward motion of the air vibrations that make our tone. Benouli's (I think) principle -- as the passage widens, velocity slows.
In general, a rapidly flaring bell is added to the end of the instrument to reduce the impedance mismatch as the sound emerges from the instrument, thus increasing the ability of the instrument to radiate sound.
- Wave Equation
- Acoustic Impedance
- Radiation Impedance
- Transmission Matrices
The sound waves propagation inside the main bore of a clarinet are described by the one-dimensional wave equation: where x {\displaystyle x} is the axis along the propagation direction. The complex solution for the sound pressure wave P ( y , t ) {\displaystyle P(y,t)} is: where k = ω / c {\displaystyle k=\omega /c} is the wave number, ω = 2 π f {\...
The acoustic input impedance Z i n ( j ω ) {\displaystyle Z_{in}(j\omega )} provides very useful information about the acoustic behavior of a clarinet in the frequency domain. The intonation and response can be inferred from the input impedance, e.g., sharper and stronger peaks indicate frequencies that are easiest to play. The input impedance (in ...
The load impedance at the open end of the cylindrical bore are represented by radiation impedance Z r {\displaystyle Z_{r}} . We assumed Z r = 0 {\displaystyle Z_{r}=0} previously when we discussed the input impedance of an ideal cylindrical pipe. Although it is very small, the radiation impedance of a real clarinet is obviously not zero. And not o...
Bore section
Since the acoustic impedance is so important for the quality and feature of a clarinet, we somehow are interested in knowing the acoustic impedance at any place along the main bore. This problem can be solved by transmission matrices method. We will see the effects of tone holes can also be incorporated into the acoustic impedance network of the instrument by introducing extra series and shunt impedances. The entire bore can be seen as a series cascade cylindrical sections, each section with...
Tonehole section
Now we deal with the tone holes. The influence of an open or closed tone hole can be represented by a network of shunt and series impedances, as shown in Figure 9. The shunt impedance Z s {\displaystyle Z_{s}} and series impedance Z a {\displaystyle Z_{a}} of a tone hole of ridius b {\displaystyle b} in a main bore of ridius a {\displaystyle a} are given by: where Z s c {\displaystyle Z_{sc}} is the shunt impedance of closed tone hole, Z s o {\displaystyle Z_{so}} is the shunt impedance of op...
Wall losses
We assumed a perfect rigid and smooth and thermally insulated wall in the previous discussions. The bore of a clarinet is of course not that ideal in the real case, so the losses due to viscous drag and thermal exchange must be taken into account. The full physical detail of thermal-viscous losses is complex and tedious and is beyond the scope of this article. Fortunately, we don't have to go to that detail if we only concerns the final effects, i.e., we just simply replacing the wave number...
On the upstream end is a mouthpiece, which has a little cup-shaped section and a constriction. At the other is a flaring section ending in a bell (the flare is longer in a tuba than in a trombone, and longer in a flugel horn than in a trumpet).
May 20, 2024 · In general, a rapidly flaring bell is added to the end of the instrument to reduce the impedance mismatch as the sound emerges from the instrument, thus increasing the ability of the instrument to radiate sound.
To increase the radiation efficiency, the end of the piping is flared into a bell. This flaring increases the radiation into the air so that the audience can hear the instrument, but even with the bell attached, the majority of the sound stays inside the instrument. The explanation of how the trumpet is constructed is now
Besides spare reeds, a small ivory or horn needle is attached to the instrument, and used to clear the reed of saliva and other debris and allows free passage of air. A metallic bell (keeḻ anaichu) forms the bottom end of the instrument.
