Emil Chacko

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The Magic of the Doppler Effect

• Emil Chacko
• Greg Della Penna
• Bryan Hahn

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Magic?

• Purpose Find the frequency of a SFCM
  (single frequency creating mechanism) due
  to a change in velocity.

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In what manner?

• Part I
• Original frequency Using a frequency sensitive
  device find the SFCMs frequency at rest.
• Masses of the SFCM and cart, small ball,
  ballistics pendulum Electric balance
• Maximum height that the pendulum moves Ruler
• Velocity of the cart after the collision
  Velocity sensor

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Manners, contd

• Part II
• Use the maximum height to find the velocity of
  the ballistics pendulum and the small ball right
  after the collision between the two.
• Use this velocity to find the velocity of the
  small ball before the collision.
• Use this velocity, with that of the car after
  the collision, to find the initial velocity of
  the car.
• Use this velocity to find the observed
  frequency of the SFCM.

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Key

• V velocity of the pendulum ball
• V2 velocity of cart SFCM
• V2i Vs
• V velocity of sound in air at room temperature
• Vo velocity of observer
• Vs velocity of source

• m1 mass of ball
• m2 mass of ballistics pendulum
• m3 mass of cart SFCM
• V1 velocity of ball
• V1i velocity of ball (before collision with
  pendulum)
• V1f velocity of ball (right after collision
  with cart)
• V1i V1f

• i initial
• f final

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Math? Boo!

• Part I
• Velocity of ballistics pendulum ball
• (1/2)(m1m2)V2 (m1m2)gy

y
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Ice Time!
http//translate.google.com/translate?hlenslfr
uhttp//colos.fcu.um.es/Cursos/Rousseau_simulatio
ns/meca/balistique.htmlprev/search3Fq3Dballist
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More Math? More boo!

• Velocity of ball
• m1V1i (m1m2)V

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Boooooo!

• Velocity of car SFCM
• m3V2i m3V2f m1V1f

http//www.physics.upenn.edu/courses/gladney/phys1
/lectures/lecture7/momentum_conservation.html
http//www.walter-fendt.de/ph11e/collision.htm
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Most Boo!

• Observed Frequency
• f f( )

http//lectureonline.cl.msu.edu/mmp/applist/doppl
er/d.htm
http//library.advanced.org/19537/java/Doppler.htm
l
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DATAR!!

• Part 1
• m1 .067 kg
• m2 .028 kg
• m3 .361 kg
• y values (equilibrium 5.5 cm)
• Trial 1 9.5 cm
• Trial 2 9.5 cm
• Trial 3 10 cm
• Trial 4 10 cm
• Trial 5 10.5 cm

• V .686 m/s
• V1i (V1f) .973 m/s
• V2i 1.05 m/s
• V2f .870 m/s

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How

• Part I
• Velocity of ballistics pendulum ball
• (1/2)( )V2 (
  )(9.8m/s2)( )
• V .686 m/s

.044m
.028kg .067 kg
.028kg .067 kg
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we

• Velocity of ball
• ( )V1i ( )(
  )
• V1i .973 m/s

.028kg .067 kg
.686 m/s
.067kg
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got

• Velocity of car SFCM
• ( )V2i ( )( ) (
  )( )
• V2i 1.05 m/s

.361 kg
.361 kg
.870 m/s
.067 kg
.973 m/s
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there!

• Observed Frequency
• f 795 hz( )

345 m/s
0 m/s
345 m/s
1.05 m/s
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Results!
f' 792.49 hz
Error 2.27!!
factual 775 hz
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Possible Sources of Error

• Lack of recording the room temperature affected
  the speed of sound in the Doppler effect equation
• Some energy in collision between the car and ball
  is lost to sound
• Noise in back ground could have thrown off
  recorded frequencies
• When reading the maximum height of the pendulum,
  round off error
• Friction between ball and Styrofoam in pendulum
  took away energy