Tuning fork frequency from resonance lengths in a tube

[rayhan619]

Homework Statement

A 40 cm long tube has 40 cm long insert that can be pulled in and out. A vibrating tuning fork is held next to the tube. as the insert is slowly pulled out the sound from the tuning fork creates standing waves in the tube when the total length is 42.5 cm, 56.7 cm, and 70.9 cm. what is the frequency of the tuning fork? The air temperature is 20 degree C.

Homework Equations

f = mv/2L

figure is attached

The Attempt at a Solution

f = 14.2
v = 343 m/s
L =(40+40) cm = 80 cm = 0.8 m

f = mv/2L = (1*343 m/s)/2*0.8 m = 214. 375 hz

got it wrong. not sure how to do it

 

[rl.bhat]

total length is 42.5 cm, 56.7 cm, and 70.9 cm.
These values indicate that the open tube resonates at every increase of equal length of the tube. At open tube this length must be half the wave length.