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# Doppler Effect

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AP Calculus AB final project.

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### Doppler Effect

1. 1. THE DOPPLER EFFECT BY: Luna Ueno Lexa Rogozinsky Shree Patel Sasha Jasty Amanda Feldman
2. 2. So… What is the Doppler Effect? <ul><li>http:// www.youtube.com/watch?v =xPLbQ9rkz1Q </li></ul><ul><li>Credits: “The Big Bang Theory” is an American sitcom created by Chuck Lorre and Bill Prady, broadcasted by CBS. </li></ul>
3. 3. CONCEPT <ul><li>Definition: An observed change in frequency of a wave of sound or light with the frequency increasing as the object gets closer to the observer and with the frequency decreasing as the source moves away from the observer </li></ul><ul><li>In other words, the change in the observed frequency of a wave when the source of the wave is moving with respect to the observer </li></ul><ul><li>The effect was first described by Christian Doppler, an Austrian physicist in the 1800’s who discovered this effect after observing the change in amplitude of a train’s siren as it passed by him </li></ul>
4. 4. SAMPLE PROBLEM The Frequency F of a fire truck siren heard by a stationary observer is given by F = where ± V represents the velocity of the accelerating truck in meters per second. Find the rate of change of F with respect to V when: a) The truck is approaching at a velocity of 30 meters per second b) The fire truck is moving away at a velocity of 30 meters per second
5. 5. Solution <ul><li>Find the derivative of F using the quotient rule: </li></ul>a) Plug in -30 1.461 b) Plug in +30 -1.016
6. 6. REAL WORLD APPLICATION <ul><li>This allows you to be able to distinguish the position of an object according to the intensity of a sound wave </li></ul><ul><li>Police use a Doppler Radar to check for speeding violations </li></ul><ul><li>Meteorologists use this to track the movement of storms- determines motion of winds and direction and velocity of hail or rain </li></ul><ul><li>Bats use this to hunt for prey-listens for echoes, reflected waves show a shift in frequency </li></ul>
7. 7. Which means… <ul><li>You can recognize the Doppler Effect when you see… </li></ul><ul><li>An ambulance driving past you; </li></ul><ul><li>An elephant running past you; </li></ul><ul><li>An elephant in an ambulance driving past you. </li></ul>
8. 8. THE END