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Wave Equations

Wave Equations. Definitions. Day 1. Amplitude Maximum deflection (the biggest x value) Measured in meters Period (T) Time for one event Measured in seconds Frequency (f) Events per second f = #events/second Measured in Hertz f = 1/T. Click for amplitude example.

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Wave Equations

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  1. Wave Equations

  2. Definitions Day 1 • Amplitude • Maximum deflection (the biggest x value) • Measured in meters • Period (T) • Time for one event • Measured in seconds • Frequency (f) • Events per second f = #events/second • Measured in Hertz • f = 1/T Click for amplitude example Hand out purple definition wksh

  3. Do pendulum lab

  4. POD • A pendulum is released from 1.0m above the table. swings from 1 to 3 and back ten times in 5 seconds. • Identify the amplitude • Calculate the period • Calculate the frequency 0.4m

  5. What changes the frequency for a pendulum? • Amplitude? (height released) No • Mass? No • Length of string Yes

  6. Periodic Motion • Any motion that repeats so it has a definite period • Pendulum • Spring • Swing • Bungee cord • waves • Sound • All periodic motion • makes waves • Has amplitude • Has period and frequency

  7. Now think about a bouncing spring • Where will the displacement be zero? • Where will the displacement be at a maximum? • What about in between? Equilibrium point Both ends of the spring (top and bottom) PE and KE changes

  8. For an oscillating spring. . . • Where is the net force the greatest? • The largest x position (F = -kx) • At the peaks where it changes direction • Where is the net force zero? • When displacement is zero • At the equilibrium – the middle

  9. For an oscillating spring. . . • Where is the velocity the greatest? • At the equilibrium – the middle • There is no net force to slow it’s motion here • Where is the velocity zero? • At the peaks because direction changes • There is a maximum force, but zero velocity

  10. Do spring lab

  11. What changes the frequency for a spring? • Amplitude? (height released) No • Mass? Yes - more mass less motion (inertia resists change) • Spring constant (k)? Yes - strong spring “jumps” back, weak spring slowly changes

  12. So frequency • For a spring ƒ = 1/(2)√(k/m) • Where k is the spring constant • M is the mass in kg • For a pendulum ƒ = 1/(2)√(g/l) • Where g is the acceleration due to gravity which is 9.8m/s/s • L is the length of the string in meters

  13. A 60kg person bungee jumps from a bridge . He bounces 10 times in 15 s. • What is the length of time for each bounce? • What is the frequency of bouncing? a) 1.5 sec b) f=0.66Hz

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