The effect you noticed is the result of the combination of Doppler effect and sound absorption.
Sound absorption in a fluid is proportional to
$exp(- \alpha \nu^2 x)$
where $\alpha$ is a dimensional constant, $x$ is the traveled path, and $\nu$ is the sound frequency.
In its own reference frame, the airplane emits always the same sound, irrespective of whether it is approaching or receding from the observer. But for the observer, the frequency of a wave (which is $\nu_0$ in the plane frame) seems $\nu_a = \nu_0/(1-v_j/c_s)$ when the airplane is approaching, and $\nu_r = \nu_0/(1-v_j/c_s)$ when the plane is receding (here $c_s$ is the sound speed and $v_j$ the airplane's speed). Thus the perceived frequency jumps by a factor
$F = \left(\frac{1+v_j/c_s}{1-v_j/c_s} \right)$
This means that the absorption coefficient, at the time when the airplane is passing overhead (thus $x \approx H$, the plane's height over the ground), jumps from
$D_a = \exp(-\alpha H \nu_0^2 /(1-v_j/c_s)^2)$
to
$D_r = \exp(-\alpha H \nu_0^2 /(1+v_j/c_s)^2)$
For typical values for the atmosphere, and the propagation of sound waves in it, this means that $D_a \ll 1$, while $D_r \approx 1$.
Hence, what is happening is that, as the airplane passes roughly overhead, the sound goes from being deeply absorbed, especially at high frequencies, to not being absorbed at all (its normal sound, as you call it). The strange sound you noticed is what you perceive as the lower frequencies are becoming less and less absorbed, and thus the sound spectrum changes.