1. Vibrations and Waves Physics I

2. Periodic Motion and Simple Harmonic Motion  Periodic Motion - motion that repeats back and forth through a central position  Simple Harmonic Motion (SHM) – periodic motion where the Force is proportional to the displacement from the equilibrium position (F  d)

3. Simple Harmonic Motion (SHM)  In Simple Harmonic Motion the Net Force at the equilibrium position is zero. When the object moves away from the equilibrium position a Restoring Force pulls the object back.  As “d”  then “F”   Examples; Spring, Pendulum

4. Simple Harmonic Motion (SHM)  Objects in SHM can be described with two quantities. Period (T) – the time needed to complete one cycle of motion Period (T) – the time needed to complete one cycle of motion Amplitude (A) – is the maximum distance the object moves from the equilibrium position Amplitude (A) – is the maximum distance the object moves from the equilibrium position

5. Springs  Hooke’s Law – the Force of a Spring is proportional to the distance from the equilibrium position  F S = kd F S = Restoring Force of the Spring F S = Restoring Force of the Spring d = displacement from the equilibrium position d = displacement from the equilibrium position k = spring constant for that particular spring k = spring constant for that particular spring

6. Period of a Spring  To find the period of a spring (T S ) in simple harmonic motion: T S = 2  (m/k) 1/2 (Square Root) T S = 2  (m/k) 1/2 (Square Root) m = mass of the spring m = mass of the spring k = spring constant k = spring constant

7. Elastic Potential Energy  Elastic PE (PE SP ) is the energy gained by an object when it is stretched or compressed.  PE SP = ½kx 2  Examples: Rubber band, Spring, Bow and Arrow  Stretching an object increases its PE SP and this energy can change to other forms like Kinetic Energy KE.

8. Pendulums  A Pendulum is a mass attached to a string or wire of length (L) that swings back and forth through the equilibrium position  A pendulum swinging through small angles is an example of SHM

9. Pendulums  Gravity is the restoring force and is proportional to the distance away from the equilibrium position  The components of gravity change as the pendulum moves back and forth resulting in F g  d

10. Period of a Pendulum  The Period of a Pendulum (T P ) can be found with; T P = 2  (L/g) 1/2 Square Root T P = 2  (L/g) 1/2 Square Root The Period of the Pendulum depends only on the length and the acceleration due to gravity (Not the mass) The Period of the Pendulum depends only on the length and the acceleration due to gravity (Not the mass)

11. Resonance  Resonance is increasing the amplitude of vibration by adding a small force at regular time intervals  Examples: Swing (Pendulum), and Sound

12. Types of Waves  Mechanical Waves -are waves that require a medium or material to pass through.  Water, sound, waves along a string. Medium could be Water, Air, String or Spring. Medium carries energy. Newton’s Law predict Motion of Mechanical Waves.

13. Types of Waves  Electromagnetic Waves -No medium is needed for these waves. They travel through space at the speed of light.  We will look only at Mechanical Waves. Easier to study!

14. Three Types of Mechanical Waves  Transverse Waves -Cause the particles in a medium to vibrate perpendicular to the direction of Motion.  Ex. Displacement of Spring is perpendicular to Motion of Wave.

15. Three Types of Mechanical Waves  Longitudinal Waves -Cause the particles of a medium to move parallel to the direction of the wave.  Surface Waves -Mixture of Transverse and Longitudinal Waves. Water on the surface of a Lake or Ocean, Displace up and down and Left and Right

16. Describing Waves  Wave Pulse - Single disturbance in a medium.  Traveling Wave - Will move along rope in a regular manner. Regular time intervals.  Crest - High point of each wave

17. Describing Waves  Trough - Low point of each wave  Period - Time for one cycle of a wave  Frequency – number of complete vibrations per second at any one point on a wave. Measured in Hertz (Hz).

18. Describing Waves  Frequency and Period are related. f=1/T or T=1/f f=1/T or T=1/f  Wavelength - Distance between 2 points in which a wave repeats itself. Wavelength is represented with the Greek letter “lambda” (  Wavelength is represented with the Greek letter “lambda” ( 

19. Describing Waves  To the find the speed of a waves.  v= d/t d =  (wavelength) t =T t =T  v=  /T or v= f  v=  /T or v= f

20. Describing Waves  Amplitude - Is the maximum displacement from the rest or equilibrium position.  To produce a larger amplitude you need to do more work. Larger amplitude means the wave has more Energy  Rate of Energy carried by a wave is proportional to the square of the Amplitude.

21. Waves at Boundaries  Speed of Mechanical Wave does not depend on Amplitude or “frequency” of the wave. It depends on properties of Medium  A Bigger Amplitude means more Energy but it moves at same speed. Amplitude does not effect speed.

22. Waves at Boundaries  Waves with a Higher frequency “f” have a shorter wavelength “ ” as long as medium remains the same.  The speed of high and low frequency waves remains the same.

23. Waves at Boundaries  Incident Wave- Original wave in First Medium  Transmitted Wave- Second wave that continues in New Medium.  Reflected Wave- Wave that moves Backwards into Old Medium.

24. Waves at Boundaries  If the difference in the Mediums is small then the Amplitude of the Transmitted wave is very similar to the Amplitude of the Incident wave and the Reflected wave has a small Amplitude.  If the difference in the Mediums is large then most of the energy is Reflected. The Reflected wave has a large Amplitude.

25. Waves at Boundaries  Whenever a wave passes from a less dense medium to a more dense medium the Reflected wave is Inverted.  Whenever a wave passes from a more dense medium to a less dense medium the Reflected wave is Upright.

26. Waves at Boundaries  If the speed of a wave increases when it passes into a new medium then wavelength “ ” also increases.  When a wave reaches a boundary some of wave is transmitted and some of the wave is reflected.  The more different the media more of the incident wave is reflected.

27. Interference of Waves  Super Position Principle - states that the displacement of a medium caused by two or more waves is the algebraic sum of the displacements caused by individual waves.  Interference - the result of the super position of two or more waves.

28. Interference of Waves  Constructive Interference (C.I.) – Occurs when the wave displacements are in the same direction. The resultant wave has an Amplitude larger than either individual wave. The waves add together.  Destructive Interference (D.I.) – Occurs when the wave displacements are in the opposite directions. The resultant wave is reduced because the waves cancel each other out.  If waves have unequal Amplitudes D.I. will not be complete. Some of wave will remain.

29. Interference of Waves  Node – Place where medium is never displaced (d = 0) produced by D.I.  Antinode – Place where maximum displacement at medium occurs (d = max) produced by C.I.  Standing Wave – Wave pattern that includes Nodes and Antinodes that cause the wave to look like it is standing still.

30. Reflection of Waves  Angle of Incidence (  i ) – angle between Incident Ray and Normal Line  Angle of Reflection (  r ) – angle between Reflected Ray and Normal Line  Law of Reflection – States that the Angle of Incident is equal to the Angle of Reflection.  i =  r  i =  r

31. Refraction of Waves  Refraction – the change in direction of waves at the boundary between two different media.

32. Diffraction of Waves  Diffraction – the spreading out of waves around the edge of a barrier.