Subsonic Jet Noise (Including Effect of Convection)
In Chap. 4, the equations for the intensity of sound and acoustic power were developed as if, due to fluctuations in the flow properties, there were a fluctuation in the quadrupole strength producing noise, but otherwise the quadrupole remained stationary
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Subsonic Jet Noise (Including Effect of Convection)
In Chap. 4, the equations for the intensity of sound and acoustic power were developed as if, due to fluctuations in the flow properties, there were a fluctuation in the quadrupole strength producing noise, but otherwise the quadrupole remained stationary in space. In this chapter, these are now modified to account for the relative velocity between the source and the observer. Motion of air or gas has two different effects on the propagation of sound. When the source and the observer (receiver) are moving relative to each other, there is a shift in the frequency and the wavelength of the radiating sound, which is called the Doppler effect and will be discussed in the following section. This is also found in the case of propagation of electromagnetic waves and is dealt with by the transformation of the coordinate by the Lorentz transformation. However, the transformation is based on the idea that there is an absolute limitation in the velocities of many bodies imposed by the velocity of propagation of electromagnetic waves. An important difference between the propagation of sound waves and the propagation of electromagnetic waves is that the velocity of energy flow for sound waves at any point is the vector sum of the velocity of sound in a quiescent atmosphere and the velocity of the propagating medium, whereas such an effect is not known for electromagnetic waves. In the presence of a wind gradient, this effects the line of propagation of sound waves such that they bend in the downstream direction (refraction of sound waves), and the sound level at the receiver is much greater when it is in a downward position than in an upwind position. This leads to a shadow region in the upwind direction, depending on the frequency of the propagating sound wave and the local velocity of the sound wave (local temperature). There is a strong reduction in intensity of the upwind direction, but it is amplified in the downwind direction. For a detailed discussion of the effect of wind and temperature gradients on the propagation of sound waves, readers are referred to Harris [4] and references therein.
T. Bose, Aerodynamic Noise: An Introduction for Physicists and Engineers, Springer Aerospace Technology 7, DOI 10.1007/978-1-4614-5019-1 5, © Springer Science+Business Media New York 2013
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5 Subsonic Jet Noise (Including Effect of Convection)
Fig. 5.1 Moving source/observer
5.1 Doppler Effect If an observer and a source of sound are not moving with respect to each other (the distance between them being r), but the latter sends sound waves with a wavelength λo , then the number of oscillations reaching the observer in a time unit is given by the frequency
νo = co /λo ,
(5.1)
where co is the velocity of propagation of the sound waves (in ambient air at rest). If only the observer is moving toward the source, then in time t the observer travels a distance of [c∞ + (V cos θ )]t = ct, and then co + (V cos θ ) co V ν= = (5.2) 1 + cos θ = νo (1 + M cos θ ),
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