# Homework Help: Resonance problem

1. Oct 4, 2005

### insertnamehere

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!!

Last edited: Oct 4, 2005
2. Oct 4, 2005

3. Oct 4, 2005

Pleasseeee!!

4. Oct 5, 2005

### mukundpa

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 $$\frac {R}{ \pi r^2}$$ m/sec.

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

So find the interval for which water rises by $$\frac {\lambda}{2}$$