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This expression is valid as long as the period of the flow fluctuations at the sound source is large compared to the time it would take a density perturbation to span the transversal area of the tube connected to the tube, which can be approximated by Ai /c, where c stands for sound speed. For flow fluctuations of the order of the KHz, and transversal areas in the millimeters, this condition is satisfied.
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This expression is valid as long as the period of the flow fluctuations at the sound source is large compared to the time it would take a density perturbation to span the transversal area of the tube connected to the tube, which can be approximated by Ai /c, where c stands for sound speed. For flow fluctuations of the order of the KHz, and transversal areas in the millimeters, this condition is satisfied.
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A monotonically decreasing r=r (L) can be used to account for losses of the sound waves in the tube, which are neglected in this work.
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A monotonically decreasing r=r (L) can be used to account for losses of the sound waves in the tube, which are neglected in this work.
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67650166583
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The right-hand side of Eq. 5 is a first-order approximation of Eq. 2 for r<1. That is, the first term in the rightmost part of Pi (t) =α Psub x-r Pi (t-T) □a Psub [x (t) -rx (t-T)] + r2 Pi (t-2T) □a. In Eq. 5, we also name δ=α Psub.
-
The right-hand side of Eq. 5 is a first-order approximation of Eq. 2 for r<1. That is, the first term in the rightmost part of Pi (t) =α Psub x-r Pi (t-T) □aα Psub [x (t) -rx (t-T)] + r2 Pi (t-2T) +□a. In Eq. 5, we also name δ=α Psub.
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27
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