Wave Behavior

1. Wave Behavior • Interference • Doppler Effect Reflection Refraction Diffraction

2. Boundary Behavior • A sound wave travelling through water reflects off the submarine and returns to its original source. • Does reflection of a wave affect the speed of the wave? • The behavior of a wave (or pulse) upon reaching the end of a medium is referred to as boundary behavior.

3. Fixed-end Reflection applet applet • Rope is connected to a pole. • The last particle is fixed at position and unable to move.

4. Fixed-end Reflection • When the incident pulse reaches the boundary: Reflected pulse in inverted A portion of energy is transmitted to the pole The disturbance returns to the source (left side)

5. Fixed-end Reflection • What happens to the wave characteristics? • Speed • Wavelength • Amplitude Remains the same Remains the same Decreases

6. Free-end Reflection applet • Rope is attached to a loosely-fit ring around the pole. • Last particle is free to move.

7. Free-end Reflection • Reflected pulse is not inverted. Speed Wavelength Amplitude Remains the same Remains the same Decreases

8. Reflection - Wave diagram Wavelength remains the same λ Law of reflection: angle i = angle r

9. Wave diagram – wave fronts These lines represent wave fronts Wave fronts is a imaginary line that joins up particles of the same phase together. Direction of wave. It is perpendicular to the wave fronts.

10. Wave diagram – wave fronts All the particles along the wave fronts are in phase. All are “crests” of a transverse wave

11. Refraction • Consider transmission of the rope wave from less dense medium ( the thin rope) towards the boundary with a more dense medium (the thick rope).

12. Refraction

13. Refraction – wave diagram applet Video: ripple tank Water waves travelling from less dense to denser medium: Speed decreases Frequency remains the same wavelength decreases

14. Refraction – wave diagram Incident wave direction Wavelength decreases as wave travels from less dense to densermedium. Refracted wave direction

15. Refraction – Beach Erosion animation headland Bay shallow deep

16. Refraction of Sound Day Sound waves bends “towards the normal” • During the day the air is warmest near the ground and cooler away from ground. • Sound wave closest to the ground is fastest, and the wave farthest above the ground is travelling the slowest. denser medium Less dense medium

17. Refraction of Sound - Day • Day time – sound bends upwards. • A "shadow zone" region created in which sound wave cannot penetrate. • Person standing in the shadow zone will not hear the sound even though he/she might be able to see the source

18. Refraction of Sound - Night Sound waves bends “away the normal” • During the night the air is cooler near the ground and warmer away from ground. • Sound wave closest to the ground is slowest, and the wave farthest above the ground is travelling the fastest. Less dense medium denser medium

19. Refraction of Sound - Night • Night time – sound bends downwards. Loud Thunder? warmer air Cooler air

20. Interference video • two waves meet while travelling along the same medium. • net effect of the two individual waves. Destructive interference Constructive interference

21. Constructive Interference applet Video: wave pool • occurs at any location along the medium where the two interfering waves have a displacement in the same direction. • as a result, the medium has a resultant displacement which is greater than the displacement of the two interfering pulses.

22. Destructive Interference applet Video: Microwave interference • occurs at any location along the medium where the two interfering waves have a displacement in the opposite direction. • resultant displacement is either zero or smaller than the original displacement of both waves.

23. After Interference? • Interestingly, the meeting of two waves along a medium does not alter the individual waves or even deviate them from their path. • two waves will meet, produce a resultant shape of the medium, and then continue on doing what they were doing before the interference.

24. Quiz 1 • Several positions along the medium are labeled with a letter. Categorize each labeled position along the medium as being a position where either constructive or destructive interference occurs.

25. ANS Constructive Interference: G, J, M , N Destructive Interference: H , I , K , L , O

26. Quiz 2 • Jimmy and Johnny are both creating a series of circular waves by jiggling their legs in the water. The waves undergo interference and create the pattern represented in the diagram at the right. The thick lines in the diagram represent wave crests and the thin lines represent wave troughs. Several of positions in the water are labeled with a letter. • Categorize each labeled position as being a position where either constructive or destructive interference occurs.

27. Quiz 2 Destructive Interference: C,D,E,F Constructive Interference: A, B

28. Standing Wave applet • A standing wave pattern results from the interference of two or more waves along the same medium. • All standing wave patterns are characterized by nodes.

29. Standing Wave - Nodes • Nodes occur when two waves interfere such that one wave is displaced upward the same amount that a second wave is displaced downward. • Destructive interference leads to a point of "no displacement." A node is a point of no displacement.

30. Standing Wave - Antinodes • There are other points along the medium which undergo vibrations between a large positive and and large negative displacement. • These are the points which undergo the maximum displacement during each vibrational cycle of the standing wave. In a sense, these points are the opposite of nodes, and so they are called antinodes.

31. Standing Wave • Standing wave can only be obtained when the proper frequency is used, such that the interference of the incident wave and the reflected wave produces specific points along the medium which appear to be standing still nodes and the antinodes • nodes and antinodes are not actually part of a wave. Recall that a standing wave is not actually a wave but rather a pattern which results from the interference of two or more waves.

32. Natural Frequency • Nearly all objects, when hit or struck or plucked or strummed or somehow disturbed, will vibrate. If you drop a stick or pencil on the floor, it will begin to vibrate. • The frequency or frequencies at which an object tends to vibrate when disturbed is the natural frequencyof the object.

33. Natural Frequency Video: singing glass Video: unbelievable music The actual frequency is dependent upon : • the properties of the material the object is made of (this affects the speed of the wave) • lengthof the material (this effects the wavelength of the wave).

34. Forced Vibration • Pluck a guitar string compared to the same string mounted on a guitar. • What is the difference? Much louder when string on the guitar is plucked. Why?

35. Forced Vibration • When the string is attached to the sound box of the guitar, the vibrating string forces the sound box to vibrate at its natural frequency. • The sound box in turn forces air particles inside the box to vibrate at the same natural frequency as the string. Sound box

36. demo Forced Vibration • The entire system (string, guitar, and enclosed air) vibrates and forces surrounding air particles into vibrational motion. • The tendency of one object to force an adjoiningobject into vibrational motion is referred to as a forced vibration.

37. Resonance Video: motor resonance Video: pendulum resonance Video: ghost swing • Video Demo

38. Resonance • Resonance occurs when one object vibrating at the same natural frequency of a second object forces that second object into vibrational motion. • Result of resonance is always a very large vibration. Tacoma Narrows bridge Washington, 1940 video

39. Resonance - Experiment • Plastic tube with air column When the natural frequency of the air column is tuned to the frequency of the vibrating tuning fork, resonance occurs and a loud sound results. Resonance occurs at odd multiples of ג/4. Why?

40. Resonance – Standing wave • When an object is forced into resonance vibrations at one of its natural frequencies, it vibrates in a manner such that a standing wave is formed within the object. • Such patterns are only created within the medium at specific frequencies of vibration. These frequencies are known as harmonic frequencies or merely harmonics.

41. Resonance – Sound waves • Demo - Chladniplate, violin bow and salt

42. Resonance – Sound waves • Pattern formed is the standing wave pattern associated with one of the natural frequencies of the Chladni plate. • Salt vibrate and tumble about the plate to reaches point along the plate which are not vibrating.(nodes)

43. Resonance – Sound waves • Music and Harmonics