The physics of wind instruments

In summary, when a tube is open at both ends and vibrating at its fundamental frequency, the air pressure is equal to ambient pressure at both ends and oscillates at its maximum in the middle. The frequency of the fundamental wavelength is twice the length of the tube. When the tube is vibrating at the second overtone frequency, the pressure can be either higher or lower at one end compared to ambient pressure, depending on which end is excited. When one end of the tube is blocked, its fundamental frequency becomes half of its original frequency. This is different from string instruments, which are easier to understand than wind instruments.
  • #1
TheLil'Turkey
66
0
In a tube (open at both ends) that's vibrating at its fundamental frequency, is the air pressure the ambient air pressure at both ends and higher in the middle, lower in the middle, or can it be either higher or lower in the middle? Why?

If the same tube is vibrating at the frequency of its second overtone (1/3 the wavelength of the fundamental frequency), can the pressure be the ambient pressure at one end and either higher or lower at the other end? If you blow on one end, does that end become the one with the regular pressure or the higher/lower one?

If one end of the tube is blocked, does its fundamental frequency then become half of what it was before?

String instruments seem so much easier to understand than wind ones.
 
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  • #2
TheLil'Turkey said:
In a tube (open at both ends) that's vibrating at its fundamental frequency, is the air pressure the ambient air pressure at both ends and higher in the middle, lower in the middle, or can it be either higher or lower in the middle? Why?

If the same tube is vibrating at the frequency of its second overtone (1/3 the wavelength of the fundamental frequency), can the pressure be the ambient pressure at one end and either higher or lower at the other end? If you blow on one end, does that end become the one with the regular pressure or the higher/lower one?

If one end of the tube is blocked, does its fundamental frequency then become half of what it was before?

String instruments seem so much easier to understand than wind ones.

For a tube open at both ends, the pressure is equal to atmospheric at both ends. It oscillates inside the tube when excited at the appropriate frequency. The lowest mode will see the maximum pressure oscillations at mid-length (this is called a pressure antinode). So the lowest-mode (fundamental) wavelength is twice the tube length. The next higher mode with have two antinodes, at the 1/4 and 3/4 length points, and will have a wavelength equal to the tube length. The pitch will be an octave higher than the fundamental. The third mode (second overtone) will have three antinodes, at the 1/6, 1/2, and 5/6 length points. The open ends are still pressure nodes (equal to atmospheric).

If you block one end of the tube, that end becomes a pressure antinode. So the wavelength of the fundamental will be 4 times the length of the tube, the next mode will have two pressure antinodes, at the 1/3 point and the closed end (assuming the closed end is at 1), the next mode will have three pressure antinodes, at the 1/5, 3/5, and closed end (again closed=1).

BBB
 
  • #3
bbbeard said:
For a tube open at both ends, the pressure is equal to atmospheric at both ends. It oscillates inside the tube when excited at the appropriate frequency. The lowest mode will see the maximum pressure oscillations at mid-length (this is called a pressure antinode). So the lowest-mode (fundamental) wavelength is twice the tube length. The next higher mode with have two antinodes, at the 1/4 and 3/4 length points, and will have a wavelength equal to the tube length. The pitch will be an octave higher than the fundamental. The third mode (second overtone) will have three antinodes, at the 1/6, 1/2, and 5/6 length points. The open ends are still pressure nodes (equal to atmospheric).

If you block one end of the tube, that end becomes a pressure antinode. So the wavelength of the fundamental will be 4 times the length of the tube, the next mode will have two pressure antinodes, at the 1/3 point and the closed end (assuming the closed end is at 1), the next mode will have three pressure antinodes, at the 1/5, 3/5, and closed end (again closed=1).

BBB
Wow. I was very confused before, but this cleared a lot of things up. I think you made one mistake though; the bolded 1/3 point should be 1/2, right?
 
  • #4
TheLil'Turkey said:
Wow. I was very confused before, but this cleared a lot of things up. I think you made one mistake though; the bolded 1/3 point should be 1/2, right?

No, it's 1/3. See attached.
 

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  • #5
That makes sense. Thank you!
 

Q: What is the physics behind sound production in wind instruments?

The physics of sound production in wind instruments is based on the vibration of air molecules. When a player blows air into the instrument, it causes the air molecules inside to vibrate at a certain frequency, creating sound waves.

Q: What role does the shape of a wind instrument play in its sound production?

The shape of a wind instrument plays a crucial role in its sound production. The length, diameter, and tapering of the instrument all affect the frequency of the sound produced. A longer instrument will produce lower frequencies, while a shorter one will produce higher frequencies.

Q: How do different playing techniques affect the sound produced by a wind instrument?

The sound produced by a wind instrument can be altered by various playing techniques, such as changing the embouchure (position of the lips), using different fingerings, and varying the air pressure. These techniques can change the pitch, volume, and tone of the sound produced.

Q: What is the difference between a woodwind and a brass instrument in terms of physics?

The main difference between woodwind and brass instruments is the way they produce sound. Woodwind instruments use a reed or a mouthpiece to create vibrations in the air, while brass instruments use the player's lips and the shape of the instrument to produce sound.

Q: How does the material of a wind instrument affect its sound?

The material of a wind instrument can affect its sound in various ways. For example, wooden instruments may produce a warmer and richer sound compared to metal instruments, which tend to have a brighter and louder sound. The thickness and density of the material can also impact the sound produced by an instrument.

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