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Homework Help: Resonance problem

  1. Oct 4, 2005 #1
    Problem with Standing Waves in Air Columns

    Hello, i'm having problems with this problem, lol...so far, i have found one of the main components of the following question, but I don't know where to go from there. please help

    Water is pumped into a tall vertical cylinder at a volume flow rate R. The radius of the cylinder is r, and at the open top of the cylinder a tuning fork is vibrating with a frequency f. As the water rises, how much time elapses between successive resonances?

    Ok, so far, this is what I got. I consider R to be V (volume) and since volume of a cylinder is pi(r^2)h where h is the height and equal to L. And since this considers harmonics, L= (wavelength)/4, therefore f= (V speed of sound)/(4L)
    So I replaced L with (Volume/area of base or R/(pi*r^2) and solved to find frequency. But i don't know where to go about finding the TIME ELAPSED!!
    Please help. Thank you
     
    Last edited: Oct 4, 2005
  2. jcsd
  3. Oct 4, 2005 #2
    Please Helpp!!!!!!
     
  4. Oct 4, 2005 #3
    Pleasseeee!!
     
  5. Oct 5, 2005 #4

    mukundpa

    User Avatar
    Homework Helper

    The water is rising in the cylinder which is behaving as a resonance column(closed organ pipe). With the rise in the level of water the length of air column is decreasing at a rate of [tex] \frac {R}{ \pi r^2} [/tex] m/sec.

    For the resonance to occur in the closed organ pipe the lengths of the air column should be [tex] (2n + 1) \frac {\lambda}{4} [/tex]
    hence the difference in the lengths for successive resonance is [tex] \frac {\lambda}{2}[/tex]

    So find the interval for which water rises by [tex] \frac {\lambda}{2}[/tex]
     
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