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Vibrations & Waves

Vibrations & Waves. Chapter 25 - This will be phun!. 2 Types of Waves. Mechanical Wave : Requires a mechanical medium Sound, water, air, springs, or ropes are examples. Electromagnetic Waves (EM) : Does not require a medium for motion to occur Light, Radio, and X-rays are examples.

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Vibrations & Waves

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  1. Vibrations & Waves Chapter 25 - This will be phun!

  2. 2 Types of Waves • Mechanical Wave: • Requires a mechanical medium • Sound, water, air, springs, or ropes are examples. • Electromagnetic Waves (EM): • Does not require a medium for motion to occur • Light, Radio, and X-rays are examples.

  3. “Making Waves”

  4. Transverse Waves • Causes the particles of the medium to vibrate perpendicularly to the direction of motion of the wave. • Piano and guitar strings are examples

  5. Longitudinal Waves • When particles of the medium move parallel to the direction of the waves. • Fluids, liquids, gases, or plasma usually transmit only longitudinal waves.

  6. Longitudinal and Transverse

  7. Longitudinal vs Transverse Waves Compression = Crest Rarefaction = Trough Energy Movement: parallel vs perpendicular Wavelength: compression + rarefaction crest + trough

  8. Surface Waves • They are a mixture of transverse and longitudinal waves. (water & Rayleigh) • The particles move both parallel and perpendicular to the direction of the wave.

  9. Wave Pulse and Traveling Wave • Wave Pulse: • A single disturbance that travels through a medium. • Traveling Wave: • Moving, periodic disturbances in a medium or field.

  10. Period • The shortest time interval during which the motion repeats itself. • Abbreviated with the capital letter,T • SI Unit: seconds (s)

  11. Frequency • The number of complete revolutions per second. • Frequency is abbreviated with a fancy ƒ. • Frequency is measured in Hertz, Hz. • A Hertz is one vibration per second (1/s).

  12. Equation Frequency and the period of a wave are related by the following equation. Frequency and Period are reciprocals of each other.

  13. Wavelength • The shortest distance between points where the wave pattern repeats itself. • The wavelength is abbreviated with the Greek letter, lambda, A: ? B: ? C: ? D: ? E: ?

  14. Wavelength The shortest distance between points where the wave pattern repeats itself. The wavelength is abbreviated with the Greek letter, lambda, A: 1 Wavelength B: 2X Amplitude C: Nodes D: Amplitude E: ½ Wavelength

  15. Vocabulary • Crests: • The high points of each wave motion. • Troughs: • The low points of each wave motion • Amplitude: • The maximum displacement from the rest or equilibrium position. • Nodes: • Where the wave crosses the equilibrium line. • Antinodes: • The bottom of the trough and the top of the crest

  16. Vocabulary Crests: The high points of each wave motion. Troughs: The low points of each wave motion Amplitude: The maximum displacement from the rest or equilibrium position. Nodes: Where the wave crosses the equilibrium line. Antinodes: The bottom of the trough and the top of the crest A&F: Crests (Antinodes) D&I: Troughs (Antinodes) B,E,G,J: Nodes

  17. To find the velocity of a wave • Wave velocity (v) is the product of the frequency (f) and wavelength (l). • To find out how fast a wave moves, you would use this equation…

  18. Amplitude and Energy • In order to produce a wave with a larger amplitude, more energy is needed. • Waves with larger amplitudes transfer more energy. • Amplitude does not affect frequency nor velocity.

  19. Waves Changing Mediums • Waves passing from one medium to another have the same frequency. • The wavelength change depends on the velocity change so that f is constant. • If the velocity increases, the wavelength increases (direct relationship).

  20. Superposition and Interference • Principle of Superposition: • Two or more waves occupying the same space. • Interference: • The result from two or more waves occupying the same space.

  21. Constructive Interference • Occurs when the wave displacements are in phase (crest meets crest or trough meets trough). • The result is a wave with a largeramplitude than the individual waves.

  22. Destructive Interference • Occurs when the wave displacements are out of phase (crest meets trough). • The result is a wave with a smalleramplitude than the individual waves. Red: wave moving right Blue: wave moving left Green: superposition (Red + Blue wave)

  23. Destructive Interference • If the pulses have unequal amplitudes, destructive interference is not complete. The pulse of the overlap is the algebraic sum of the two pulses. Red: wave moving right Blue: wave moving left Green: superposition (Red + Blue wave)

  24. Standing Wave • When the nodes and antinodes are stationary, the wave appears to be standing still. • If you increase the frequency of a standing wave, you will see more nodes.

  25. Superposition of Waves • A. Two pulses traveling in opposite directions • B. Two sine waves traveling in the same direction, but at different speeds • C. Two sine waves traveling in opposite directions. http://paws.kettering.edu/~drussell/Demos/superposition/superposition.html

  26. Nodes and Antinodes • Node: • The point in the medium that is completely undisturbed at all times. A node is produced by destructive interference of waves • Antinode: • The point of maximum displacement. An antinode is formed from constructive interference.

  27. Harmonics

  28. Let’s check for understanding… The number of nodes in the standing wave shown in the diagram at the right is a. 6 b. 7 c. 8 d. 14

  29. Let’s check for understanding… The number of nodes in the standing wave shown in the diagram at the right is c. 8

  30. Let’s check for understanding… The number of antinodes in the standing wave shown in the diagram at the right is a. 6 b. 7 c. 8 d. 14

  31. Let’s check for understanding… The number of antinodes in the standing wave shown in the diagram at the right is b. 7

  32. Let’s check for understanding… In the standing wave shown, a. What is the amplitude? b. What is its wavelength? c. How many nodes are there? d. How many antinodes are there?

  33. Let’s check for understanding… In the standing wave shown, a. What is the amplitude? 10 cm b. What is its wavelength? c. How many nodes are there? d. How many antinodes are there?

  34. Let’s check for understanding… In the standing wave shown, a. What is the amplitude? 10 cm b. What is its wavelength? 1 m c. How many nodes are there? d. How many antinodes are there?

  35. Let’s check for understanding… In the standing wave shown, a. What is the amplitude? 10 cm b. What is its wavelength? 1 m c. How many nodes are there? 6 d. How many antinodes are there?

  36. Let’s check for understanding… In the standing wave shown, a. What is the amplitude? 10 cm b. What is its wavelength? 1 m c. How many nodes are there? 6 d. How many antinodes are there? 5

  37. Reflection of Waves • Normal: • A line that is drawn perpendicular to the barrier (green). • Angle of Incidence: • The angle between the incidence ray and the normal. • Angle of Reflection: • The angle between the normal and the reflected ray. >I = >R

  38. Refraction of Waves • Refraction: • The change in the direction of waves at the boundary between two different media.

  39. Diffraction of Waves • Diffraction: • The spreading of waves around the edge of a barrier. • Diffraction occurs when waves meet a small obstacle. • They can bend around the obstacle, producing waves behind it.

  40. Problem-Solving

  41. Springs • Spring Constant

  42. Spring Constant (stiffness) • A spring stretches 18 centimeters when a 56 Newton weight is suspended from it. What is the spring constant? • Find: k • Givens: d (x) = 18 cm = 0.18 m F = 56 N Formula: k = F d Solution: 310 N/m

  43. Springs • Potential Energy in a Spring

  44. Period of a Pendulum • Pendulum

  45. Using a Pendulum • A pendulum with a length of 36.9 centimeters has a period of 1.22 seconds. What is the acceleration due to gravity at the pendulum’s location? • Find: a (g) • Givens: d = 36.9 cm = 0.369 m T = 1.22 s Formula: g = 4p2L T2 Solution: 9.78 m/s2

  46. Velocity, Wavelength, Frequency and Period Relationships • Wavelength

  47. Wavelength • An 855 Hertz disturbance moves through an iron rail at a speed of 5130 meters per second. What is the wavelength of the disturbance? • Find: l • Givens: f = 855 Hz v = 5130 m/s Formula: l = v f Solution: 6.00 m

  48. Velocity, Wavelength, Frequency and Period Relationships • Period

  49. Period • An 855 Hertz disturbance moves through an iron rail at a speed of 5130 meters per second. What is the period of the disturbance? • Find: T • Givens: f = 855 Hz Formula: T = 1 f Solution: 0.00117 s

  50. Velocity, Wavelength, Frequency and Period Relationships • Velocity

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