Bob M clearly has way too much free time on his hands:

I am at the top of a hill sitting on my bicycle. I tune my horn to 
a440. I proceed down the hill (still playing the concert a)  where a 
highly-sensitive tuner is positioned to determine the pitch of my 
instrument at precisely the moment I have achieved 10 miles per hour. 
What is the frequency of my a as I go speeding by?

************
Your pitch would rise as you approach the tuner and fall as you  
go away from it.  So when you are even with the tuner, you will 
be playing 440. 

In doing this calculation, I have neglected relativistic effects
(according to a stationary observer, time dilation lowers your 
frequency ) and  distance effects (unless you run over the tuner,
then when you are even with the tuner, it still will be 
receiving sound from an earlier moment, when you were
approaching the tuner, thus raising the perceived frequency.)

This answer is also valid if the tuner is going downhill on your
bicycle while you play horn at the foot of the hill.  It even works
if (while going uphill on your bicycle) you pass the tuner, though
that involves pedal tones.

Gotta go,
Cabbage

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