Intro to Waves

1. Intro to Waves

2. Intro to Waves • All things wiggle/vibrate/oscillate. • A wave is a wiggle in time. • The equilibrium is the resting position of a wave. • An object is at rest when experiencing a balance of forces. • An object will remain in this position until it is disturbed. • Forced vibration: The force which sets the resting object into motion.

3. Intro to Waves • Waves transfer energywithout transferring matter. • Two types of waves: • Mechanical (through a medium) • Electromagnetic (through a “vacuum”, an empty space)

4. Mediums • A medium is a substance or material that carries the wave from its source to other locations. • The medium consists of particles that interact with each other. • Each particle interacts with the adjacent particle, which allows the disturbance to travel through the medium • Examples: air, metal, string, people • Waves travel at different speeds based on the medium

5. Mechanical Waves • Requires a medium • Ex: water, sound, slinky, stadium • 2 types: • Transverse – particles of the medium move perpendicular to the direction that the wave moves • Longitudinal – particles of the medium move parallel to the direction that the wave moves

6. Transverse Wave: • Wave particles move perpendicular to the direction the wave travels • Ex: strings of a musical instrument Perpendicular to the direction of travel Direction of travel

7. Longitudinal Wave: • Particles vibrate parallel to the direction the wave travels • Ex: sound wave Direction of travel Particles vibrate parallel to the direction of travel

8. Parts of a transverse wave Crest Wavelength (ג) amplitude Equilibrium Position Wavelength (ג) amplitude Wavelength (ג) Trough

9. Parts of a Transverse Wave – Sine Curve • Crest- highest point on a wave, maximum positive displacement from equilibrium • Trough- lowest point on a wave, maximum negative displacement from equilibrium • Equilibrium position- resting position • Amplitude- from the equilibrium position to the crest or trough • Wavelength – distance between any two identical points on a wave

10. Periodic Motion • A wave moves over the same path over the course of time • The object not only repeats the same motion, it does so in a regular fashion • If it takes 3.2 sec to complete the 1st cycle, it will take 3.2 sec to complete the 2nd, 3rd, 4th… • A motion that is regular and repeating is called periodic motion

11. Damping • Some energy is being dissipated over the course of time. • The mechanical energy of the vibrating object is lost to other objects. • The amount of displacement from its equilibrium position changes slightly with each vibration cycle. • Eventually the vibrations will cease.

12. Pulse vs. Wave • Pulse: A single disturbance of the medium particles. • The energy passes through the medium in a single cycle and then the disturbance ceases. • Wave: A repeated and periodic disturbance of the medium particles. • A wave vibrates back and forth over a period of time.

13. Wave pulse is a single wave disturbance • Wave train (continuous wave) - is a series of pulses at intervals

14. Speed of waves • Speed: how fast an object is moving. • For a wave, speed is the distance traveled by a given point on the wave, such as the crest, in a given time interval • V = d/t • Ex: If a crest moves 20 m in 10 sec, what is the speed? • V = 20/10 • V = 2 m/s

15. Frequency • Frequency (f) is a measure of the number of cycles per unit of time. • Measures in hertz (Hz) • F = # cycles/time

16. Period • Period (p) is the time for a particle on a medium to make one complete vibrational cycle. • Measured in seconds • P = time/# cycles

17. Frequency and Period • Frequency and Period are inversely related • P = 1/F F = 1/P

18. Relationship between Wavelength, Frequency and Wave Speed (velocity)

19. velocity ( v ): speed of the wave • unit: m/s (meter/second) • frequency ( f ): number of wave vibrations per second • unit: Hz (hertz) • wavelength ( ג ): length of one wave (crest to crest or trough to trough) • unit: m (meter)

20. Relationship between frequency and wavelength: • Wavelength and frequency are inversely related • As frequency goes up the wavelength gets shorter (assuming no change in velocity)

21. Amplitude • Amplitude is a measure of the amount of energy carried by a wave • High energy = large amplitude • Low energy = small amplitude

22. Parts of a Longitudinal Wave: • Compression- point where the particles are closest together • Rarefaction- point where the particles are furthest apart Rarefaction Compression

23. Wave Boundary Behavior • As a wave travels through a medium it will often reach the end of the medium and encounter an obstacle or another medium • Boundary – the interface of the 2 media • Boundary behavior – the behavior of a wave upon reaching the end of a medium

24. Wave Interactions • Reflection • Refraction • Diffraction

25. Wave interactions Reflection: • The bouncing back of a wave when it encounters a new medium or boundary • Ex: light off a mirror, or sound echo • Incident wave- incoming wave • Reflected wave – the wave that returns

26. Fixed End Reflection • A fixed boundary is one not allowed to move

27. Fixed End Reflection • Reflected wave is inverted (upside down) WHY? • Speed of the reflected pulse is the same as incident pulse – WHY? • Wavelength is the same – WHY? • Amplitude of the reflected pulse is LESS than the incident wave – WHY?

28. Flexible End Reflection • A flexible boundary is allowed to move • Waves reflected off a flexible boundary are upright.

29. Flexible End Reflection • Speed of the reflected pulse is the same as incident pulse • Wavelength is the same • Amplitude of the reflected pulse is LESS than the incident wave

30. Transmission of pulse in different mediums • Wave speed differs in different types of media • Waves are faster in less dense media • At the boundary, waves will either reflect back or transmit through the other medium

31. Less to more dense media

32. Less to More Dense media • If a pulse crosses a boundary from LESS to MORE dense medium: • The reflected pulse will be inverted • The transmitted pulse will be displaced upwards – transmitted pulses are NEVER inverted • The transmitted pulse (more dense) is traveling slower than the reflected pulse (less dense) • Transmitted pulse has a smaller wavelength than the reflected pulse • Speed and wavelength are the same for the reflected and incident pulse

33. More to Less Dense

34. More to Less Dense • Reflected pulse will NOT be inverted • Transmitted pulse is NEVER inverted • Transmitted pulse (less dense) is traveling faster than reflected pulse (more dense) • Transmitted pulse has a larger wavelength • Speed and wavelength of the reflected and incident pulse are the same

35. Summary: • Wave speed is always greatest in least dense material • Wavelength is always greatest in least dense material • Frequency of a wave is not altered by crossing a boundary • Reflected pulse becomes inverted when wave goes from less dense to more dense • Amplitude of incident pulse is always greater than amplitude of the reflected pulse.

36. Reflection • Law of Reflection: The angle of incidence is equal to the angle of reflection

37. Refraction • The bending of a wave path as it enters a new medium • Caused by difference in speed of the new medium • When crossing a boundary into a different medium, the wavelength decreases • The frequency stays the same • The decrease in wavelength causes a decrease in the velocity

38. Diffraction • Spreading of waves around edges or through an opening of a boundary • Is greatest when size of opening is smaller than wavelength The amount of diffraction (sharpness of bending) increases with increasing wavelength and decreases with decreasing wavelength.

39. Superposition Principle of Superposition: • Displacement of a medium by two or more waves is the algebraic sum of the displacements of the waves alone

40. Interference of Waves • Result of the superposition of two or more waves meeting while traveling along the same medium. • Constructive- when the wave displacements are in the same direction; amplitudes add • Destructive – when the waves have opposite amplitudes; amplitudes subtract • Only temporary as paths cross

41. Constructive interference Only temporary as paths cross

42. Destructive interference Only temporary as paths cross

43. Standing Wave • A wave that appears to be standing still • Result from the interference between the incident wave and the reflected wave • The point of no displacement is the node • The point of maximum displacement is the antinode Node Antinode

44. Standing Waves • Standing waves are produced only at specific frequencies, called “harmonics” • Different frequencies create different standing wave patterns:

45. 1st harmonic pattern • 2 nodes and 1 antinode • Simplest harmonic pattern • Low frequencies 2nd harmonic pattern • 3 nodes and 2 antinodes • 2 times the frequency as 1st 3rd harmonic pattern • 4 nodes and 3 antinodes

46. Standing waves • Other ways to indicate the patterns:

47. Standing Waves • Each node is separated by the adjacent node by a distance that is equal to ½ of a wavelength. • So if the following length below is 1.2 m long – determine the wavelength of a complete wave.

48. Sound Waves • Sound waves are produced by a vibrating object . • Sound waves are longitudinal mechanical waves. • Often demonstrated with a tuning fork – as tines vibrate, they disturb the surrounding air molecules

49. Sound as a Longitudinal Wave • Individual particles of medium move parallel to the direction of the wave • As particles push on adjacent particles, some regions are created where particles are pressed together (high pressure) and in some regions they are spread apart (low pressure).

50. Sound waves • Compressions – the areas of high pressure • Rarefactions – the areas of low pressure • Since there is a repeating pattern of compressions and rarefactions, sound waves are also called “pressure waves” • A wavelength is the distance from compression to compression (or rarefaction to rarefaction)