- #1
mewmew
- 113
- 0
Well I am having some serious troubles with chapter 6 from French's book on vibrations and waves. Here are the things I am having trouble with.
1. Show that for a vibration of an air column an open end represents a condition of zero pressure change during oscillation and hence a place of maximum movement of the air.
I really have no clue how to even start this one. I can always choose my function in e[x,t]=f[x]Cos[wt] to be f[x] = A*Cos[wx/v] so that at x = 0 we have the max amplitude but that doesn't really hold for each end and doesn't really seem to do a good job.
2. A stretched string of mass m, length L, and tension T is driven by a source at each end, having the same frequency(f) and amplitude (A) but Pi radians out of phase, what is the smallest possible value of w consistent with stationary vibrations of the string?
This one I wanted to set up like a longer string with fixed ends and just have the driving forces be regular oscillations "inside" of the longer string. This doesn't seem like a good way of doing it am I think I should be able to solve it differently. The only other way I tried was to go about it like a normal problem and set my boundary conditions up as A*Sin[f] and A*Cos[f] but this got me stuck it seems. as I couldn't figure anything out after setting C*Sin(wx/v) equal of the above boundary conditions.
3.in accordance to the above how do I deal with the boundary condtions of waves fixed at say one end or no ends, or driven on both ends, it seems like their are tons of different boundary conditions and each have a different way of solving, but I am really having trouble figuring out how to go about this.
Thanks for any help.
1. Show that for a vibration of an air column an open end represents a condition of zero pressure change during oscillation and hence a place of maximum movement of the air.
I really have no clue how to even start this one. I can always choose my function in e[x,t]=f[x]Cos[wt] to be f[x] = A*Cos[wx/v] so that at x = 0 we have the max amplitude but that doesn't really hold for each end and doesn't really seem to do a good job.
2. A stretched string of mass m, length L, and tension T is driven by a source at each end, having the same frequency(f) and amplitude (A) but Pi radians out of phase, what is the smallest possible value of w consistent with stationary vibrations of the string?
This one I wanted to set up like a longer string with fixed ends and just have the driving forces be regular oscillations "inside" of the longer string. This doesn't seem like a good way of doing it am I think I should be able to solve it differently. The only other way I tried was to go about it like a normal problem and set my boundary conditions up as A*Sin[f] and A*Cos[f] but this got me stuck it seems. as I couldn't figure anything out after setting C*Sin(wx/v) equal of the above boundary conditions.
3.in accordance to the above how do I deal with the boundary condtions of waves fixed at say one end or no ends, or driven on both ends, it seems like their are tons of different boundary conditions and each have a different way of solving, but I am really having trouble figuring out how to go about this.
Thanks for any help.