- #1
Apophilius
- 14
- 0
I've encountered a bit of a conceptual problem in my studies and I was hoping someone could help me out with this:
I understand that the longitudinal sound wave takes the form of the equation s(x,t) = smcos(kx +/- wt), and that the equation for pressure variance produced by the sound wave takes the equation p(x,t) = pmsin(kx +/- wt). I also understand that the velocity of an air element experiencing a wave can be found by taking the partial derivative of the s(x,t) equation with respect to whatever variable you feel like, and that the velocity will be out of phase from your pressure variance equation by pi radians. What I do NOT understand is this.
In simple harmonic motion (the kind of motion I understand a sound wave to be in) your acceleration and therefore your force is out of phase with displacement by pi radians, not velocity. At maximum displacement from equilibrium, you should experience your greatest acceleration and therefore your greatest force (since in simple harmonic motion, f = cx). With sound waves, however, you experience your greatest pressure at equilibrium, when your velocity is greatest - an idea counter-intuitive to the principles of simple harmonic motion.
Where I feel I've gone wrong is here: perhaps the pressure variance is not the force causing the air elements to oscillate, but if that were the case, where does the force come from?
I understand that the longitudinal sound wave takes the form of the equation s(x,t) = smcos(kx +/- wt), and that the equation for pressure variance produced by the sound wave takes the equation p(x,t) = pmsin(kx +/- wt). I also understand that the velocity of an air element experiencing a wave can be found by taking the partial derivative of the s(x,t) equation with respect to whatever variable you feel like, and that the velocity will be out of phase from your pressure variance equation by pi radians. What I do NOT understand is this.
In simple harmonic motion (the kind of motion I understand a sound wave to be in) your acceleration and therefore your force is out of phase with displacement by pi radians, not velocity. At maximum displacement from equilibrium, you should experience your greatest acceleration and therefore your greatest force (since in simple harmonic motion, f = cx). With sound waves, however, you experience your greatest pressure at equilibrium, when your velocity is greatest - an idea counter-intuitive to the principles of simple harmonic motion.
Where I feel I've gone wrong is here: perhaps the pressure variance is not the force causing the air elements to oscillate, but if that were the case, where does the force come from?
