I Frequencies of standing waves in a straw

[steven george]

I am a physics teacher and I my class is currently studying sound waves. I had my class make some noise makers with straws as shown here. http://www.physics.org/interact/physics-to-go/straw-oboes/

We measured the frequencies coming from the straws and they seem to act like a pipe open at both ends since all the harmonics are present. The frequencies seem to be much lower than we would expect though. I had students use the length of the straw and the fundamental frequency to find the speed of sound. Most of them were getting answers between 120 and 145 m/s.

We considered the straw length to be half a wavelength and then multiplied the wavelength by the fundamental frequency to find the speed. Am I missing something here, or is there some reason that this behaves differently than a typical open ended air column?

Thanks for any help!

 

[nasu]

This kind of instrument ("reeds" instruments, like oboe, clarinet) behaves usually like closed tube at the mouth end.
So your fundamental mode has a wavelength which is about 4 times the length of the tube. (With the end correction, the factor is a little more than 4)
So you will get speed values that are not too bad.

 

[steven george]

Thanks! I had suspected that it would behave like a closed tube at the mouth end but if that was the case I would expect to see only odd numbered harmonics. We saw all the harmonics so I am still a bit puzzled by the whole thing.

 

[nasu]

How did you measure the frequencies?

 

[steven george]

How did you measure the frequencies?

I use a fantastic program called Zelscope.

 

[Paul Doherty]

Hi Steven

I repeated your experiment and got similar results.
I used audacity to measure the spectrum of the straw oboe and saw all the harmonics as expected from a tube open at both ends , not the odd harmonics predicted by the physics of oboes.
Then I looked at the fundamental frequency and the resulting speed of sound was extremely low assuming a tube open at both ends and even substantially low assuming a tube closed at one end and open at the other.

I don't see many people posting their spectra, tube lengths and spectra on line.
our 10 cm straw oboe resonated at many frequencies depending on how hard we blow but the lowest frequency at reasonable flow was 344 Hz and the highest was 409 Hz , these frequencies are far lower than the resonance of the straw if we assume either an open or closed end.

I do not know what would cause this.

 

[steven george]

Thanks for your input. I'm still hoping to find out what the problem is.

 

[olivermsun]

An oboe air column behaves like that one of an open pipe at both ends, so it should have the even harmonics.

The interesting thing relative to the results you are finding is that an oboe has length 62 cm, but lowest note around 233 Hz.

 

[steven george]

An oboe air column behaves like that one of an open pipe at both ends, so it should have the even harmonics.

The interesting thing relative to the results you are finding is that an oboe has length 62 cm, but lowest note around 233 Hz.

Thanks. Do you have any explanation for the discrpencies? The numbers you give would give a wavelength of 1.24 m (a little more than that when you account for end correction. That would give us a speed of under 300 m/s, which is much too low. The results with straws were much, much worse than this.

 

[olivermsun]

I don't know ... it's a real mystery to me.

The oboe numbers don't seem so far off if you give a 10-15% allowance for end effects, the actual geometry of the oboe, maybe viscous effects, etc. There is a more rigorous way to predict the frequencies that is detailed in Plitnick and Strong (1979): http://scitation.aip.org/content/asa/journal/jasa/65/3/10.1121/1.382503

The straw is interesting though. I will think about it some more tomorrow.

 

[Tom.G]

With the high aspect ratio of a straw, I expect the acoustic impedance to be rather high; increasing the effective mass of the enclosed air. (see: http://press.princeton.edu/chapters/s9912.pdf) The increased effective mass would lower the resonant frequency, as with a spring-and-mass oscillator.

This site may also be of some interest: https://www.nde-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/acousticimpedance.htm

 

[sophiecentaur]

I'm wondering about the impedance of an oscillating reed. The simple analysis of a vibrating column or string assume that the ends are perfect open or short circuits. Could the substantial mass ( but not infinite) be introducing a further end effect? Woodwind instruments are not high Q resonators so their natural frequencies would probably depend a lot on the oscillating mechanism as well as the resonant air column.

 

[Paul Doherty]

With the high aspect ratio of a straw, I expect the acoustic impedance to be rather high; increasing the effective mass of the enclosed air. (see: http://press.princeton.edu/chapters/s9912.pdf) The increased effective mass would lower the resonant frequency, as with a spring-and-mass oscillator.

This site may also be of some interest: https://www.nde-ed.org/EducationResources/CommunityCollege/Ultrasonics/Physics/acousticimpedance.htm

Thanks for the links the Princeton book does a great job of describing acoustical impedance. Paul Doherty