Re: Doppler Effect Question

[Gary Karshner <karshner@STMARYTX.EDU>]

> If an observer is stationary and a car drives around the observer in a
> perfect circle, will the observer perceive any change in pitch?  Or, will
> the sound of the horn maintain a constant pitch because the radius of the
> circle is constant?  At first I said that the pitch would remain constant
> because the observer and sound source are always a constant distance from
> one another.  But then I began to think about the car being at different
> distances from each ear and wasn't sure whether there would be a change
> in frequency or not.  Can anyone help out?  This is an algebra/trig-based
> course.

        Your muddying the water.  Your first answer is correct as far as it goes.
I demonstrate the Doppler effect with an apparatus I build using one of
those obnoxious solid state beepers from Radio Shack. (As my musical
friends tell me, they are obnoxious because they produce a pure sine wave
and not a musical note, but this makes them ideal for this demonstration.)
It is mounted on a small piece of wood with an nine volt battery, The wood
is fastened to a stout cord so that it can be sung around my head. The
students in the class hear the Doppler effect as it changes speed in their
direction. I, at the center, hear only a small effect since my ears are not
exactly at the center of rotation.
        One of the real powers of the method of analysis we use in physics is that
we are always making simplifications, when you start relaxing those the
answers can quickly become murky. Since I have two ears, I probably can
hear some phase variation as well, but I have always attributed most of the
change to the small velocity component because the ear is not at the
center. If I make the string truly at the center of my head will I also
hear a beat do to the opposite Doppler effects in each ear? Into the mud we go!

Gary
Gary Karshner

St. Mary's University
San Antonio, Texas
KARSHNER@STMARYTX.EDU