What Causes Small Scale Patterns at Antinodes in Standing Sound Waves?

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The small scale striated vibration patterns observed at the antinodes in a Kundt's tube are likely caused by higher harmonics of sound waves, which create closely spaced accumulations of cork dust. Despite the expectation that the fundamental frequency would dominate, the distinct scale of the observed patterns suggests a wavelength of about 1 cm, corresponding to a frequency around 33,000 Hz. A Fourier analysis conducted outside the tube showed that these higher harmonics were not prominent, raising questions about their origin. The movement of particles in these small scale ripples occurs perpendicular to the tube's axis, differing from initial expectations of back-and-forth motion. Overall, the phenomenon is consistent across various observations, indicating it is not merely an experimental artifact.
donc
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Homework Statement



I just used the Kundt's tube to illustrate the effect of a standing sound wave in a glas tube. The characteristic nodes and antinodes were perfectly visible and some small scale striated vibration patterns at the antinodes were prominent. What is the physical explanation for these small scale patterns?

Thanks in advance.
 
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donc said:

Homework Statement



I just used the Kundt's tube to illustrate the effect of a standing sound wave in a glas tube. The characteristic nodes and antinodes were perfectly visible and some small scale striated vibration patterns at the antinodes were prominent. What is the physical explanation for these small scale patterns?

Thanks in advance.

Welcome to the forums.

They are most probably higher harmonics. Higher harmonics sound waves are surely present in the tube and they will create additional accumulation of cork dust that will be more closely spaced than the main ones, and they will be of smaller amplitude.
 
Thanks for answering.

Observing higher harmonics has been my first idea as well, however, shouldn't be the first harmonic, i.e. half the wavelength, be the strongest? The observed small scale variations have a very distinct scale. Maybe I should have given more details before. My tube has a length of 0.61m)hence I get for example a resonance for at ~420Hz, i.e. lambda~0.81m. The small scales have a wavelength of about lambda~1cm, i.e. ~33000Hz. Furthermore I did a Fourier analysis of the sound spectrum *outside* of the tube and none of the higher harmonics were very prominent.

Before I performed the experiment I imagined to see the particles moving back and forth rapidly in the antinodes and being more or less motionless in the nodes. However, the particles are moving in these small scale
ripples *perpendicular* to the tube's axis.

Finally, I want to emphazise that these ripples aren't by far an artefact of my experimental design (which is admitably quite simple!) it can also bee seen on all images I have seen so far. As an example I would like you to have a look here:
http://www.physics.montana.edu/demonstrations/video/3_oscillationandwaves/demos/pics/kundtstube3.JPG

I hope somebody can help me with the explanation of these observations.
 
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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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