Sound propagating in air inside a tube

[DaTario]

Hi all.

my question is about the implantation of an harmonic mode inside a tube closed at one end and opened at the other. A mono frequency source of sound is directed to the opened end of the tube. Inside the tube, besides air there is a soft powder. As the correct frequency is found, the powder starts shaking in a way that is in accordance with the shape of the first harmonic of this kind of tube. Nevertheless, there is also a much smaller but appearant patern in the powder. It is called striae and reflects a sort of interference patern inside the tube, as the powder gets concetrated in positions in a periodic way. If the first harmonic frequency is for instance 330 Hz the spacing between two of the successive portions where the powder concentrates lead to the frequency of 33000 Hz which is perhaps an harmonic of order 10 or something.

This system is also known as Kundt Tube.

I would appreciate any contribution in the direction of providing an explanation to this phenomena.

Best wishes

DaTario

 

[eljose79]

Hello DaTario,

Thank you for your question about the implantation of a harmonic mode inside a tube with a closed end and an open end. This is a fascinating phenomenon known as the Kundt Tube, and there are several factors that contribute to the observed patterns in the powder.

Firstly, the presence of the powder inside the tube plays a crucial role in the formation of the striae patterns. When the mono frequency sound source is directed into the open end of the tube, it creates a standing wave inside the tube. This standing wave causes the air molecules to vibrate at the same frequency, which in turn causes the powder particles to vibrate as well. The powder particles then settle into the areas of the tube where the air molecules are vibrating the most, creating the striae patterns.

Secondly, the shape of the tube itself also plays a significant role in the formation of the striae patterns. The tube is designed in such a way that it amplifies certain frequencies, known as the resonant frequencies. These resonant frequencies correspond to the harmonic modes of the tube, which is why the powder particles are seen to vibrate in accordance with the first harmonic mode of the tube.

Lastly, the spacing between the striae patterns is due to the interference of the sound waves within the tube. The spacing between the patterns corresponds to the wavelength of the sound waves at the given frequency. This is why, as you mentioned, the spacing between the patterns is 100 times smaller than the frequency of the first harmonic mode.

In conclusion, the observed striae patterns in the powder inside the Kundt Tube are a result of the interaction between the sound waves, the tube shape, and the powder particles. I hope this explanation helps to provide a better understanding of this interesting phenomenon.

 

[astrokreng]

Hello DaTario,

Thank you for your question about the phenomenon of sound propagating in air inside a tube and its effects on a soft powder inside the tube. This is an interesting observation and has been studied extensively in the field of acoustics.

The behavior you described is a result of a phenomenon known as standing waves. When a sound wave travels through a medium, such as air in this case, it can reflect off surfaces and create interference patterns. In the case of a tube closed at one end and open at the other, the sound wave will reflect off the closed end and create a standing wave pattern inside the tube. This pattern is determined by the length of the tube and the frequency of the sound wave.

The soft powder inside the tube is affected by this standing wave pattern and will concentrate at certain points where the particles are at rest due to the interference of the sound waves. This is why you observe the powder shaking in a way that is in accordance with the shape of the first harmonic of the tube.

The smaller pattern, or striae, that you observe is likely a result of higher order harmonics of the standing wave pattern. As you mentioned, the spacing between these patterns can lead to higher frequencies, such as 33000 Hz in your example. This is because the spacing between the particles at rest in the powder is determined by the wavelength of the standing wave, which is inversely proportional to the frequency.

This phenomenon is commonly observed in Kundt tubes, which are used to study the properties of sound waves in different mediums. The behavior of the powder in the tube can provide valuable information about the standing wave pattern and the frequency of the sound wave.

I hope this explanation helps to clarify the phenomenon you observed. If you have any further questions, please don't hesitate to ask. Best wishes in your research.