Frequency dependence of far field condition I am analyzing accelerometer data collected at a drill rig, at the top of the drill string. The drill bit acts an acoustic source; the acoustic waves travel through the drill pipe from the bit to the sensor.

Based on Aki & Richards (1980), far field begins when the distance from source to receiver r exceeds "many wavelengths". Other authors (e.g. Poletto et al., 2020) express the transition between far field and near field as r~$\lambda$/2$\pi$.
Considering a peak frequency fpeak of 2Hz (consistent with the drill's rotational speed of 120rpm) and compressional velocity c of 5,000m/s in steel, I find the wavelength $\lambda$:
$\lambda$=c/fpeak=5000/2=2500m.
For a source-receiver distance r of 40m, r<$\lambda$ (and also r<$\lambda$/2$\pi$): the far field condition is not met.
However, I am also interested in the drill string's resonance frequency. Let's assume in this example that fresonance is 120Hz. This leads to:
$\lambda$=c/fresonance=5000/120=41.66m.
In this example, r~$\lambda$ and r>$\lambda$/2$\pi$.
How can this result be interpreted?

*

*Should I understand that the measured signal is a mix between near and far field signals?

*Is it even relevant to consider the source-recever distance r when dealing with the resonance frequency? After all, the source of the 120Hz signal is no longer the drill bit but the pipe itself, oscillating at its resonance frequency.

 A: Bottom Line Up Front: There is no far field for your problem.
The "far field" is a feature of homogeneous two- and three-dimensional background domains, whereas your system is effectively one-dimensional.  In the "far field" the acoustic energy propagates only radially away from the source region.  In one-dimensional systems all energy propagates in that dimension, and so either the entire domain is the far field or none of it is the far field.  Furthermore, since your domain is finite, there are going to be reflections from the receiver side of the drill line, so you are going to have energy propagating both ways throughout the entire line, so you really should not be thinking of this system in terms of near and far fields.
Now, if the primary signal you were looking at propagated through the earth (i.e., was a seismic wave), you could start thinking about far versus near field behavior, because the earth is a full three-dimensional system.  However, I am guessing that your signal is dominated by the transmission along the line.
Edit: Please see the comments for further discussion and (perhaps) clarification.
