Question

The experiment has not been done yet. I am not sure where to get the value for lambda?

146 Sound Resonance in a Tube Overview Sound waves are considered longitudinal waves. That is, the molecules (air molecules for instance) will oscillate about their equilibrium positions in the direction of the wave (disturbance). If a tuning fork vibrates and held over an open ended tube, which is closed at the bottom, it will send a sound wave down the tube. This wave will be reflected at the tube's closed end, interference between the reflected wave and the next wave traveling down the tube thus creating the possibility of a standing wave being set up in the air column in the tube. The figure below shows three such standing waves. speud ot cound inair 331.5 m The relationship between the (variable) lengths of the air column in the tube L and the wavelengths of the standing waves λ are: The first value is the shortest length of tube for resonance of sound with fixed frequency. The second value corresponds to the second shortest length and so forth. In the above equation, Lcom is a correcting factor (due to the fact that the maximum amplitude has to occur just outside the tube).

Answer 1

Here $\lambda$  is the wavelength of the sound wave. And the relation between wavelength and the length of the tube for close end organ tube is given by equation. i.e. .

$L = (2n + 1) \, \frac{\lambda}{4}$ ; Where n = 0 , 1 , 2 , 3 , 4 , ..............

N denotes the node and A denotes the anti node in the diagram.

But it has been found that the wave actually does not starts from the end of the pipe, there is always some error in wave formation. And this end correction is given by

  $L_{corr.} = \Delta L = 0.6 r$

Where, r is radius of the tube (measure it in the lab).

So,   

$L + L_{corr.}= (2n + 1) \, \frac{\lambda}{4}$

or,   $\lambda = \frac{4}{(2n + 1)} \, [L + L_{corr.}]$ , n = 0 , 1 , 2 ,3 , .............

Now using this equation you can calculate the wavelength of the wave with end correction.

For any doubt please comment and please give an up vote. Thank you.