What Is the Frequency of the Tuning Fork in a Resonating Water Tube Experiment?

[dagitt]

Homework Statement

1. A vertical tube with a tap at the base is filled with water, and a tuning fork vibrates over its mouth. As the water level is lowered in the tube, resonance is heard when the water level has dropped 20 cm, and again after 60 cm of distance exists from the water to the top of the tube. What is the frequency of the tuning fork?

2. If you drop a stone into a well that is d = 129.5 m deep, as illustrated in the figure below, how soon after you drop the stone will you hear it hit the bottom of the well?

Homework Equations

V = f * Wavelength
(f = frequency in Hz)

T = 1 / f
(T =period in sec.)

Speed of sound = 340.29 m/s

The Attempt at a Solution

1. i just don't understand it..i'm assuming the 20cm and 60cm are wavelengths? why am i given two? if i plug these into the equation V = f * Wavelength (using speed of sound for V), i get 2 different answers...and according to my webassign, neither are right. i think I'm doing something wrong, because i generally just don't understand how to set up this prob.. :(

2. Wavelength = 129.5 m, V = 340.29 m/s. Solve for frequency.
F = 2.63 Hz, plug into Period Formula.
T = .38 sec. But this is the wrong answer according to Webassign.

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any or all help appreciated. i really just suck at anything math related.
thanks so much

 

[Chewy0087]

1) Have you studied standing waves yet? If not you'll need to look them up as they're the key here.

Look at this standing wave;

http://www1.union.edu/newmanj/lasers/Light%20as%20a%20Wave/standing%20wave2.JPG

The resonance will occur when the wave hits the water on a maximum, i.e after 1/4 of a wavelength, and after 3/4 of the wavelength, do you see why?

2) The wavelength is not 129.5m, there's no reason why it should be. I can't see any reason why you'd need to consider frequency/wavelength here, use the simple relation time = distance / speed