Is the tuba an open or closed pipe?

[songoku]

Homework Statement

When a tuba played, the player makes a buzzing sound and blows into one end of a tube that has an effective length of 3.5 m. The other end of the tube is open. If speed of sound is 343 m/s, what is the lowest frequency of tuba?
a. 49 Hz
b. 12 Hz
c. 24 Hz
d. 8 Hz
e. 16 Hz

Relevant Equations

Open tube: f = nv / 2L

Closed tube: f = (2n-1)v / 4L

Is tuba open or closed tube? I google the picture of tuba and I think it is closed tube (one end open to air and one end put into mouth so it becomes closed end). Using formula of closed pipe, I get f = 24.5 Hz but the answer is 49 Hz which is obtained by using formula of open pipe.
How to determine whether an instrument is open or closed pipe?
Thanks

 

[haruspex]

In a half open pipe with no internal source of sound, at the open end there is maximum movement of air (amplitude of longitudinal oscillation) and minimum variation in pressure (stays at atmospheric). At the closed end, the opposite is true; the air has nowhere to move.
So the question is, which situation applies at the mouthpiece of the tuba?
There's a useful discussion at https://newt.phys.unsw.edu.au/jw/flutes.v.clarinets.html.

 

[songoku]

In a half open pipe with no internal source of sound, at the open end there is maximum movement of air (amplitude of longitudinal oscillation) and minimum variation in pressure (stays at atmospheric). At the closed end, the opposite is true; the air has nowhere to move.
So the question is, which situation applies at the mouthpiece of the tuba?
There's a useful discussion at https://newt.phys.unsw.edu.au/jw/flutes.v.clarinets.html.

In my opinion, for all instrument where one end is put into mouth, the mouthpiece part will be closed end because air can not move freely but I read in the link that the shape of the air column affects the sound. Flute and clarinet is cylindrical but oboes, bassoons and saxophones is conical and the sound produced will be similar to open pipe (flute) rather than closed pipe (clarinet).

Tuba is similar to saxophones so I think that is the reason why the answer is 49 Hz.

Thanks

 

[haruspex]

In my opinion, for all instrument where one end is put into mouth, the mouthpiece part will be closed end because air can not move freely but I read in the link that the shape of the air column affects the sound. Flute and clarinet is cylindrical but oboes, bassoons and saxophones is conical and the sound produced will be similar to open pipe (flute) rather than closed pipe (clarinet).

Tuba is similar to saxophones so I think that is the reason why the answer is 49 Hz.

Thanks

I reached the opposite conclusion. A tuba player does not blow across an open hole as a flautist does, so it should be more like the oboe case. My bet is (c), as you had originally.

 

[songoku]

I reached the opposite conclusion. A tuba player does not blow across an open hole as a flautist does, so it should be more like the oboe case. My bet is (c), as you had originally.

This is from the link given: https://newt.phys.unsw.edu.au/jw/woodwind.html

Conical bores: oboes, bassoons and saxophones
What about oboes, bassoons and saxophones? Like the clarinet, they are closed at one end and open at the other, but the difference is that their air columns are in the shape of a cone. The resulting pressure and air motion vibrations are shown in the right hand diagram. When these waves get out into the outside world, they have the same frequencies as those from an open pipe of the same length. So an oboe, which is about the same length as the flute or the clarinet, has a lowest note close to that of the flute and, like the flute, it plays all of the harmonic series.

I read somewhere in your link the reason (maybe) is because in conical shape instrument, at the mouthpiece part the displacement of air particles is not completely zero but I can not find that paragraph right now

 

[haruspex]

This is from the link given: https://newt.phys.unsw.edu.au/jw/woodwind.html

Conical bores: oboes, bassoons and saxophones
What about oboes, bassoons and saxophones? Like the clarinet, they are closed at one end and open at the other, but the difference is that their air columns are in the shape of a cone. The resulting pressure and air motion vibrations are shown in the right hand diagram. When these waves get out into the outside world, they have the same frequencies as those from an open pipe of the same length. So an oboe, which is about the same length as the flute or the clarinet, has a lowest note close to that of the flute and, like the flute, it plays all of the harmonic series.

I read somewhere in your link the reason (maybe) is because in conical shape instrument, at the mouthpiece part the displacement of air particles is not completely zero but I can not find that paragraph right now

Ok, I read that, and it does make it clear that cones behave like open tubes, but I cannot follow the explanation.

 

[songoku]

Ok, I read that, and it does make it clear that cones behave like open tubes, but I cannot follow the explanation.

Neither can I

I think maybe it is because the shape of the wave given in the link (comparison between open, closed, and cone).

Would you still bet on (C)?

Thanks

 

[haruspex]

Would you still bet on (C)?

Thanks

No, I am prepared to accept that cones behave like open ended tubes. Just wish I understood why. It certainly is not apparent from those diagrams.
It does hint that it's to do with the boundary condition, which will lead to the sum of a Fourier series.

 

[songoku]

Thank you very much haruspex