Abstract
We are all aware that electricity is needed to operate an audio amplifier. We casually say that we cannot get something for nothing. We pay the electric company an amount that is based upon the number of kilowatt-hours of electricity used. In fundamental physics terms, electricity is a form of energy that is needed to power and operate an amplifier. The expenses of the electric company include the production of electrical energy from other forms of energy and the transmission of this form of energy from the electrical generator plants to your home. Thus, there are many forms of energy. And, energy can change from one form to another, as from electrical energy to the kinetic energy of a vibrating loudspeaker. However the total energy remains constant, which is a statement of the law of conservation of energy.
We introduce related the physical parameters—power (how energy is distributed over time) and intensity (how power is distributed over space), and discuss the parameters in the context of sound and light. The decibel level enables us to deal with the enormous range of sound intensities that human beings can hear and not feel pain. And finally, we discuss attenuation of sound intensity in space and in time.
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Notes
- 1.
We can estimate the energy per unit length as follows: A unit length has a mass m = μ(1) = μ. Its average speed should be a bit less than the maximum velocity v m. Thus, its KE should be a bit less than (1∕2)mv m 2 = (1∕2)μv m 2. This turns out to be the exact answer; it includes the PE too. Of course, KE=PE=constant.
Recall that v m = 2πfA (see Eq. (4.10)). Thus, the energy per unit length is proportional to the square of the amplitude A, as in the case of the energy of a standing wave.
- 2.
The mere existence of sunspots tells us that the emission of light from the SUN cannot be perfectly isotropic.
- 3.
The mathematical method is known as a Fourier Transform .
- 4.
- 5.
In Chap. 14 we will introduce a different spectral intensity I(λ): the spectral intensity with respect to the wavelength. The two spectral intensities are related. In fact there is an equation that expresses this relationship. With v being the wave velocity, we have
$$\displaystyle \begin{aligned} {\mathbf{I}}(f) = \frac{\lambda ^2}{\text{v}} \text{I}(\lambda){}. \end{aligned} $$(4.28) - 6.
Compare this linear mass density with that of a vibrating string.
- 7.
Noisy sound is often used in the waiting room of a medical doctor or a psychotherapist to maintain the privacy of the patients. The noise is not typically white noise.
- 8.
Coincidentally, the range of sensitivity and tolerance of vision to light intensities is also understood to be about twelve orders of magnitude, from ∼ 10−10 W/m2 to ∼ 100 W/m2.
- 9.
An excellent website for appreciating changes in sound levels is http://www.phys.unsw.edu.au/~jw/dB.html.
- 10.
If you examine the graphs carefully you will note that the peak of the graph lies at a lower frequency for a higher attenuation. This change is not a mistake but reflects the actual behavior.
- 11.
It is essential to keep in mind that even in the absence of attenuation, the intensity of a wave that is emitted by a point source will decrease according to the “inverse square law” of Eq. (4.27). Attenuation will produce an additional contribution to the decrease of the intensity with increasing distance from the point source.
- 12.
It is also often referred to as the attenuation coefficient .
- 13.
Here is the proof: The attenuation length is the distance over which the amplitude decreases by a factor of two. The intensity will drop by a factor of four, corresponding to ΔSL = −10 log 4 ≈−6-dB. We must then have α L ×attenuation length ≈ 6, so that α L ≈6/attenuation length.
- 14.
The graph was produced using the standard ISO 9613-1:1993. See http://www.iso.org/iso/catalogue_detail.htm?csnumber=17426. I obtained the formula from the website (2-2-2011): http://www.sengpielaudio.com/AirdampingFormula.htm. I am grateful to Eberhard Sengpiel for his help. Sadly, he passed away in 2014.
- 15.
For more information on the reverberation time see the website: http://www.yrbe.edu.on.ca/~mdhs/music/oac_proj97/music/reverb.html. You will be able to calculate the reverberation time of a room given the volume of the room and the area and absorption constant of each surface within the room.
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Gunther, L. (2019). Energy. In: The Physics of Music and Color. Springer, Cham. https://doi.org/10.1007/978-3-030-19219-8_4
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DOI: https://doi.org/10.1007/978-3-030-19219-8_4
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