What is the velocity of standing waves in a pipe based on resonance distances?

[Karol]

Homework Statement

A tube is filled with air at 77⁰C, one end open and on the other a piston. in the open end a tuning fork oscillates with 500[Hz].
The piston is set to different positions and at the distances of 18, 55.5 and 93 cm from the open end there is resonance. find the velocity of the waves.

Homework Equations

[itex]\lambda[/itex]=wave length, u=velocity: [itex]\lambda=\frac{u}{f}[/itex]

The Attempt at a Solution

I understand only one wave length is created, otherwise there will be different velocities.
For the shortest distance: [itex]\lambda=4\cdot 18[cm]=72[cm][/itex]
For the middle distance: [itex]\lambda=\frac{4}{3}\cdot 55.5[cm]=74[cm][/itex]
And for the longest: [itex]\lambda=\frac{4}{5}\cdot 93[cm]=74.4[cm][/itex]
I took the approximate mean of these wavelength: [itex]0.73[m]=\frac{u}{500}\rightarrow u=360[/itex]
Is that correct?

 

[haruspex]

There is usually an "end effect" at the open end, which slightly changes the effective length. So consider the tube to be effectively longer by some constant x in each case. You will find that this gives a quite consistent result (and slightly larger than you have calculated).