Doppler puzzle

[John Delmore]

Wow.  I see this topic (and A442 conductors-LOL) have been batted around all
weekend.  Some thoughts:
 
We don't have enough data to determine the velocity.  However, if we make
some assumptions, we can make a fair guess.  So, let's assume that
conditions are right to give a standard speed of sound of 343 m/s.  Let us
further assume that the pitch measured is A440.  And, one more assumption:
both measurements are taken at a distance of 5 meters from the truck.
 
Okay, the Doppler formula is fsubd=fsube(1+v/u), where fsubd is the observed
frequency, fsube is the emitted frequency, v is the observers velocity, and
u is the speed of the sound waves, when the observer is moving toward the
source.  When the observer is moving away from the source, the sign of the
"v/u" term is negative.  A bit of mathematical gymnastics gives
((fsubd/fsube)-1)*343=v
 
So, when you're cycling toward the truck, your velocity is 2.081 m/s, or
4.65 mph.
When you're cycling away from the truck, your velocity is 1.925 m/s, or 4.31
mph.
Your velocity has decreased by 0.156 m/s over 10 meters, so you are slowing
at a rate of 0.0156 m/s.
 
The reason you are slowing, under these conditions, is that 10 cents sharp
does not equal 10 cents flat!!  
 
G#4= 440/1.0595=415.29;  440-415.29=24.71; 24.71/10=2.471 which is the
frequency difference 10 cents flat of A440.
A#4= 440* 1.0595=466.18;  466.18-440=26.18;  26.18/10= 2.618, frequency
difference 10 cents sharp of A440.
 
If you had measured A220, instead, your respective velocities would be 2.042
m/s, 1.918 m/s, and the rate of decrease in velocity would be 0.0124 m/s.
 
New puzzle?  How far would our 95 pound, pencil-necked wisp of an A442
conductor fly if you shoved the Steinway D at him with an acceleration of 2
m/s/s from 2 meters away?  Assume standard conditions.
 
John "Doomed to think like a Chemist forever" Delmore
 
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