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Waves

Waves. Hooke’s Law. Robert Hooke 1678 F elastic = k x F elastic – elastic force (Newtons) k – spring constant (N/m) x – displacement (meters). Spring Constant. Measures the stiffness of the spring

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Waves

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  1. Waves

  2. Hooke’s Law Robert Hooke 1678 Felastic = k x Felastic – elastic force (Newtons) k – spring constant (N/m) x – displacement (meters)

  3. Spring Constant • Measures the stiffness of the spring • The greater the value of the k means a stiffer spring because a greater force is needed to stretch or compress that spring

  4. Hooke’s Law ex: Fel = k x #1 #2 k = F / x #1 k = 1N / 1 cm K = 1 N /cm #2 k = 2 N/2 cm K = 1 N/cm

  5. Plot Hooke’s Law from the previous information.What is the spring constant?

  6. Spring Constants • More information • Hooke’s Law Problems - homework

  7. Simple Harmonic Motion A vibration about an equilibrium position (in which a restoring force is proportional to displacement from equilibrium) F and a max F and a max v max

  8. The motion of Earth orbiting the sun is periodic. Is this motion simple harmonic? Why or why not? No; because Earth does not oscillate about an equilibrium position

  9. What is equilibrium, amplitude, period and frequency?

  10. Amplitude The maximum displacement from equilibrium

  11. Period The time that it takes a complete cycle to occur Measured in seconds T = 1 / f

  12. frequency The number of cycles or vibrations per unit of time Measured in Hertz ( Hz)= 1 / s f = 1 / T

  13. What is equilibrium, amplitude, period and frequency?

  14. What is the equilibrium of the spring?

  15. Period of a Pendulum or spring Pendulum T = 2 pL / g L = length(m) g= gravity( 10 m/s2) Spring T = 2 p m / k M= mass (kg) k = spring constant(N/m)

  16. Pendulum Ex: You need to know the height of a tower, but darkness obscures the ceiling. You note that a pendulum extending from the ceiling almost touches the floor and that its period is 12 s. How tall is the tower?What is the frequency of the pendulum? T = 2 pL / g (T) 2 = (2 pL / g)2 T 2 = 4 p2L / g L = gT 2 = 10 m/s2(12s)2 4 p2 4 p2 L = 37 m f = 1 / T = 1/ 12 = 0.08 Hz

  17. Spring Ex: A 5 N weight oscillates on a spring that has a displacement of 45 cm. What is the period of the spring?What is the frequency? k = f / x = 5 N / 0.45 m = 11 N / m T = 2pm/k = 2p.5kg/ 11N/m = 1.3 s f = 1 / T = 1 / 1.3 s = 0.77 Hz Pendulum and Spring Problems

  18. Types of Waves • Mechanical – a wave that propogates through a deformable elastic medium (needs a medium to travel) 2. Electromagnetic – do not a medium to travel

  19. Mechanical Waves Longitudinal waves - Waves move parallel to the wave direction EX: Sound Wave

  20. Electromagnetic Wave Transverse wave - Waves move perpendicular to the wave direction EX: Light Wave

  21. Pulse Wave Throwing a stone in a pond would be a pulse

  22. Speed of a Wave Speed of a mechanical wave is constant for any given medium Temperature determines speed V = f l V = velocity (m/s) F = frequency ( Hz) l = wavlength ( m)

  23. Wave Speed EX: A piano string tuned to middle C vibrates with a frequency of 262 Hz. Assuming the speed of sound is 343 m/s, find the wavelength of the sound waves produced by the string. V = f l f = v / l f = 343 m/s = 1.31 262 Hz

  24. Waves Anatomy Go to the following website to answer the questions. • Transverse Waves 1. Define a transverse wave 2. Draw and label the parts of a transverse wave 3. Define the parts

  25. Waves Anatomy Go to the following website to answer the questions. • Longitudinal Wave 1. Define a longitudinal wave 2. Draw and label the parts of a longitudinal wave 3. Define the parts

  26. Standing Wave Draw a standing wave labeling the nodes and antinodes • Make your own standing waves

  27. Harmonics Draw a 1st, 2nd and 3rdHarmonic

  28. Reflection- Study the animations to determine the difference between a fixed and free reflection • Fixed • Free

  29. Interference • 1. Define Constructive and Destructive Interference • 2. Adjust the points make a crest and trough, on the left and right. Hit the run button and see what happens. • http://id.mind.net/~zona/mstm/physics/waves/interference/intrfrnc.html

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