Abstract
The prime theme of this chapter is reflection of (sound) waves at interfaces between two media with different wave velocities (or different acoustical impedances). Such reflections are used in, apart from other situations, ultrasound imaging in medicine, e.g. of foetuses during pregnancy. If a wave moves in an extended medium with reflective boundaries at both ends, a wave of arbitrary shape will go back and forth repeatedly with a fixed time period determined by the wave velocity and the distance between the reflecting ends. We argue that this lies at the core of musical instruments, and not pure standing waves, used as the paradigm in most physics textbooks. We then present the tone scale and go on to define sound intensity, both physically and in relation to human hearing. The chapter ends with a discussion of beats, Doppler shifts and shock waves.
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Notes
- 1.
Both from the positive and the negative half of the frequency domain, due to folding in Fourier transform.
- 2.
There are details to the movement of a wave on a guitar string not mentioned here. These are easier to understand when we use numerical methods to calculate wave movements in Chap. 8.
References
Unknown, http://amath.colorado.edu/outreach/demos/music/MathMusicSlides.pdf. Accessed 18 February 2012
Lindosland, http://en.wikipedia.org/wiki/Equal-loudness_contour. Accessed April 2018
Lindosland, http://en.wikipedia.org/wiki/A-weighting. Accessed April 2018
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Vistnes, A.I. (2018). Sound. In: Physics of Oscillations and Waves. Undergraduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-72314-3_7
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DOI: https://doi.org/10.1007/978-3-319-72314-3_7
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Online ISBN: 978-3-319-72314-3
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