We do support doppler on 2D objects, you just need to set the object’s position using rigidbody velocity instead of animations or transforms, which is the same for 3D objects.
I do see the value in having it based on transform though as it would mean doppler would work for animations / the Unity timeline etc. I have bumped the feature request and created a documentation task to provide an example of how to implement doppler using rigidbody.
For anyone finding this in the future, I adapted @GeoffAngus implementation to a more up to date version of Unity and Fmod and I also changed the logic of how it works a bit. In my version, you can set each emitter to use kinematic velocity, regardless of having a rigidbody.
See my blog post about it, there is also a link to the GitHub project: Using Fmod Doppler on Unity without a rigidbody — Javier Zúmer - Sound Design
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