There is no general method to establish a correspondence between the two measurements.

To establish a "correspondence" you will need characterization and modelling tools. There is also conditions on the tested material.

In a Kundt's tube, the acoustic excitation is plane waves at normal incidence thus the TL should rather be called normal Sound Transmission Loss (nSTL).

You also have samples with small dimensions and this will tremendously impact your nSTL at low frequencies (when the wavelength in air is very much larger than these dimensions). Indeed, the nSTL can reach high values at low frequencies as long wavelengths will not be able to propagate through a small sized sample and will be reflected. This is a measurement artifact you will not see (or to a lesser extent) in ISO 140-3 measurements.

When the frequency increases you should find a nSTL following the mass-law behavior.

At even higher frequencies you might find bending vibrations of your homogeneous sample. From the frequency positions of these vibrations you can estimate the elastic parameters of your samples. Of course this is easier if your sample is made of an isotropic material and its first bending frequency is below the highest frequency of plane waves assumption in the Kundt's tube. Honestly, if one of these 2 conditions is not fulfilled, forget the Kundt's tube.

If everything is OK at the previous step, from the mass and elastic parameters of your sample estimated from a Kundt's tube measurement you can estimate the sound transmission loss for a larger sample (~ 10 square meters is required by ISO 140-3) and for a diffuse sound field with a modeling tool.

Finally, you're right, there is no ISO standard for the measurement of the normal Sound Transmission Loss while there is the ASTM E2611. The ISO is aware of this point and a working group should start a discussion about it in the next few months.

Thank you Luc for your complete answer.

As for the required conditions you mentioned, I don't know if the first bending frequency of plywood is below the highest frequency of plane waves assumption in Kundt's tube. Anyway plywood is an anisotropic material, so the first condition is not fulfilled and according to your answer this impedes to find a correspondence.

What is the input noise source input used in Kundt's tube for muffler transmission loss measurement?

I was looking to get same input data for CAE analysis.