Subject: telegraph equation
Don't recall studying this (i.e. telegraph equation...I'm quite familiar with Doppler). But it is interesting.

https://phys.org/news/2024-05-...

With telecommunications in mind, the telegraph equation was then developed to describe how electric current propagates with attenuation along one spatial dimension.

...

Solutions of the ordinary telegraph equation show features typical of the Doppler effect. They show the presence of a clear, sharp frequency inflection, corresponding to the moment when the source passes the observer and there is an instantaneous, abrupt change in the pitch of the sound recorded by the observer.

Interesting that they see possible medical applications, specifically heat transport.