Finding the Original Frequency of a Vibrating Tuning Fork

[Haftred]

A vibrating tuning fork is held above a column of air [...] The shortest length of an air column that produces resonance is L(1) - 0.25 m. The next length that produces resonsnace is L(2) - 0.80 m. 343 m/s is what I will use for sound. How can I find the original frequency of the tuning fork?

The original problem can be found here: (Number 3)

http://www.collegeboard.com/prod_downloads/ap/students/physics/ap04_frq_physics_b_b.pdf

 

[OlderDan]

Your minus signs are supposed to be equal signs. An explanation with some pictures worth a thousand words can be found here.

http://hyperphysics.phy-astr.gsu.edu/hbase/waves/clocol.html#c1

If you click on the "Resonance tube experiment" you can even put in your numbers to explore the solution for the ideal case. The problem as stated seems to be throwing you a curve. If the first length of air is 0.25m, the second length of air should ideally be three times that, or 0.75m. Apparently they are expecting you to assume there is deviation from ideal behavior because of the diameter of the tube, and use the difference between 0.80m and 0.25 m to come up with the half-wavelength. There is in fact such an "effective length" effect, briefly described in this description of the experiment.

http://world.casio.com/edu/resources/program_lib/ea200/pdf/07_p26_27.pdf

 

[thepatientmental]

To find the original frequency of the tuning fork, we can use the formula v = fλ, where v is the speed of sound (343 m/s), f is the frequency, and λ is the wavelength. We know that the shortest length of the column of air that produces resonance is L(1) - 0.25 m, so we can use this length to find the corresponding wavelength.

λ = 4(L(1) - 0.25) = 4(0.25) = 1 m

Now, we can plug in the values for v and λ into the formula to solve for the original frequency:

343 m/s = f(1 m)

f = 343 Hz

Therefore, the original frequency of the tuning fork is 343 Hz. This frequency is the same for both L(1) and L(2) because the wavelength is the same for both lengths. This means that the tuning fork is producing a standing wave with a node at the open end of the column of air.