Abstract
While the vibrating strings of guitars and violins are plainly visible, the sound that they produce in air is invisible. We often associate sound with air because we are used to hearing sounds that reach our ears from the air. We also learn that in the absence of air, sound cannot propagate—movies with sound propagating in outer space, not withstanding. The fact that air is so transparent is not the issue here: Sound travels through liquids such as water and solids such as steel, as well as other gases such as air; nevertheless, we cannot see sound propagating through liquids or solids either. So, what is sound? That is the first subject of this chapter. Once we understand the nature of sound, we will go on to study the modes of vibration of air that is contained in pipes, that is, air columns. These are the basic components for all wind instruments, such as the recorder, flute, and trumpet.
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Notes
- 1.
Another way to appreciate this observation is to note that if we were to take a volume of air and compress it so that all the molecules are just touching each other, the volume would be reduced by a factor of 103 = 1000.
- 2.
The following website [12-26-2010) http://comp.uark.edu/~jgeabana/mol_dyn/] has an animation that shows a collection of particles moving in a square chamber. You can choose the number and size of the particles. You can also run the animation slow enough to be able to follow a single molecule in order to see how far it travels before colliding with another molecule.
- 3.
The exact expression for the mean free path is \((\sqrt {2} ~\pi \times \text{number density} \times \text{diameter}^2)^{-1}\) . Also, note that if we were to distribute football players in a three-dimensional array of boxes, each side being 10-yards, the mean free path turns out to be about 1000-yards or a bit over one-half of a mile!
- 4.
Here is a beautiful animation that displays the collisions of molecules on a piston. [12-26-2010 http://wilsonspirit.com/] You can vary the number of molecules in the chamber. You can move the piston so as to change the volume so as to change the collision rate with the piston as well as the pressure. Finally, you can vary the temperature so that the speed of the molecules varies. A shortcoming of the animation is that it omits intermolecular collisions.
- 5.
As a person gets older and/or subjects himself/herself to loud sounds such as rock music, the upper limit goes down. In the author’s testing of students from 1973 to 2000, the limit for most students has dropped from about 22,000-Hz to about 18,000-Hz.
- 6.
It is rare to find a man-made device that can handle such a huge range of inputs.
- 7.
More precisely,
$$\displaystyle \begin{aligned} v \approx \sqrt {\frac{kT}{m} } \end{aligned} $$(3.10)where k is Boltzmann’s constant, T is the absolute temperature (temperature in degrees Celsius + 273), and m is the mass of a molecule.
- 8.
We have restricted our attention to pipes with a relatively small diameter only because in this case the frequency spectrum of the modes is a harmonic series. The larger the ratio of the diameter to the length, the greater the deviation of the spectrum from a harmonic series.
- 9.
Physical review, vol. 73, p. 383, 1948.
- 10.
Some organ pipes have a diameter so large and such a high frequency and therefore small wavelength that this condition can be violated. Levine and Schwinger calculated the error for a great range of frequencies.
- 11.
We will see Helmholtz’s name in Chap. 11, in connection with his seminal studies of hearing, which are represented in his grand treatise On the Sensations of Tone. He is famous for his major contribution in the development of the Principle of Conservation of Energy , to be discussed in Chap. 4. And finally, he is also the inventor of the ophthalmoscope , which is used to examine the interior of the eye.
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Gunther, L. (2019). The Nature of Sound. In: The Physics of Music and Color. Springer, Cham. https://doi.org/10.1007/978-3-030-19219-8_3
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DOI: https://doi.org/10.1007/978-3-030-19219-8_3
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