```Computer Interfacing: Frequency Measurement - The Doppler Effect

John Bozovsky

Objective
To use computer interfacing to measure velocity using the Doppler Shift with
sound.

Apparatus
The Apple IIe computer
The Frequency Meter program from Vernier Software
A microphone amplifier circuit using a schmidt trigger which I
constructed from instructions supplied with the software.

Strategy
The microphone circuit will be set up to monitor frequency-
clamped to a pole and facing outward.  The computer program will be chosen to
measure frequency and display it on the monitor in large print.  Several devices
can now be sounded within the proximity of the microphone--tuning forks, various
musical instruments, etc.
A discussion will now be generated by asking the class for a method of
measuring the speed of an object [or person] moving across the front of the room.
It is expected that someone will soon suggest the direct measurement of
displacement and time to be divided to give: v=d/t.  A volunteer will now be asked
to actually perform this movement while distance and time are measured using a
meter stick and stopwatch.  The formula will now be used to determine the speed v.
Now, a more exotic method will be suggested.  A ball with a sounding Sonic
Alert inside will be thrown back and forth among the class members.  It will be
noticed that a change in the frequency of sound is caused by the relative motion
of the ball with respect to the listener: It will be noted that the frequency
increases during the approach and decreases during the receding of the ball away
from the listener.  This change in frequency caused by relative motion is called
the Doppler Effect which is demonstrated by the formula:
v            f: the frequency detected by
f=  ------ fs             the listener
v-vs
fs: the actual frequency
produced by the source

Now for the action.                         v: the velocity of sound:
Once again the volunteer                           [345 m/sec]
will run across the front of the
room but this time with a bell              vs: the velocity of the source
attached to him.  While distance
and time are directly measured to yield v=d/t as before, the computer will be
instructed to measure the frequency it hears and to plot this data on a graph as
the running person approaches the microphone.  This frequency during approach is
'f' in the above formula.  The bell is now held motionless directly in front of
the microphone and the computer while it measures this frequency as 'fs'. All of
this data [including the known speed of sound] can now be used to calculate 'vs',
the speed of the runner and compare it with the direct result obtained from v=d/t.

THE MEASUREMENT OF IMPULSE
DURING A COLLISION

Objective
To use computer interfacing to determine the impulse during a collision.

2
Apparatus
Air Track and glider
The Apple IIe computer and a Pasco photogate
The Voltage Plotter program from Vernier Software
A voltage input unit
Bridge and amplifier circuits
Two strain gauges attached to a bar of spring steel
The instructions for the above circuitry are supplied along
with the Voltage Plotter software

Strategy
An air track is set up with a single glider.  The photogate is now set up at
one end of the track.  A  beam of light is produced on one side of the photogate
and is detected by a sensor on the other side of the device.  The computer is set
to measure the time duration of the eclipsing of the beam caused by the passage of
the glider through the photogate.  Knowledge of the length of the glider 'd' and
this time of passage 't' can be used to determine the speed of the glider: v=d/t.
If this value is multiplied by the mass of the glider,  the result is the glider's
momentum: p=mv.
By this time in the class, it will have  been established that momentum is
conserved.  That is, the total momentum before a collision equals the total
momentum after collision.  But what happens to the momentum during the collision?
[I could merely tell the students the answer to this question, but I wouldn't want
to be too impulsive.]
Here is where the second interfacing device enters the demonstration.   The
strain gauge bar is mounted above the far end of the air track slightly beyond the
position of the photogate.  The glider is set in motion as before from the
opposite end of the track, and is allowed to impact the strain gauge bar causing
it to flex.   This bending causes the two strain gauges mounted on the top and
bottom of the bar to change resistance which is detected by the computer as a
change in voltage.  The computer program is calibrated to measure this flexing in
terms of the force causing the bar to bend.  The computer is now instructed to
plot this changing force on a graph as a function of time.  Force multiplied  by
time can now be determined  as the area under  the plotted curve.  This
relationship  is known as the impulse=ft, and can be compared with the total
change in momentum of the glider.  Hopefully the results will show that the total
momentum before collision equals the total impulse during collision which in turn
equals the  total momentum after the collision.

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