Transmission & Reflections

1. Transmission & Reflections • Consider a pulse moving through a medium - perhaps through a rope or a slinky. What happens to the pulse when it reaches the end of that medium? (Assume the end is fixed)

2. ` • The pulse becomes inverted upon reflecting off the fixed end. • That is, a pulse with an upward displacement will reflect off the end and return with a downward displacement.

3. Now consider a free-end The pulse reflects off the free end and returns with the same direction of displacement. That is, a pulse with an upward displacement will reflect off the end and return with an upward displacement.

4. In both fixed end and free end reflection there is no change in frequency or wavelength. There is also no change in the speed of the pulse since the medium is the same.

5. Fast to Slow • A pulse (and a wave) carries energy through a medium from one location to another. But when the pulse reaches the end of the medium, where does the energy go? Does the energy disappear? Or does the energy pass into the new medium?

6. reflected pulse is inverted • the reflected pulse has a smaller amplitude than the incident pulse • the amplitude is representative of the energy carried by a wave • the reflected pulse must have less energy than the transmitted pulse • the energy of the reflected pulse (and thus its amplitude) would always be less than the energy of the incident pulse • the speed and the wavelength of the incident pulse are the same as the speed and the wavelength of the reflected pulse • wave speed depends upon the properties of the medium

7. the transmitted pulse is not inverted • in fact inversion only occurs for the reflected pulse • the transmitted pulse has a smaller speed and a smaller wavelength than the incident pulse

8. Slow to Fast Medium (More dense to less dense Medium) The fast medium acts like a free end and the reflected wave is not inverted. The transmitted wave is not inverted, travels with increased speed and wavelength and has a diminished amplitude. Incident Pulse Fast Medium Slow Medium Reflected Pulse Transmitted pulse

9. 6.6 Interference of Waves Wave interference occurs when two waves act simultaneously on the particles of a medium. There are two types of interference: constructive and destructive. Destructive interference occurs when a crest meets a trough. Constructive interference occurs when crests meet crests (supercrests) or troughs meet troughs (supertroughs).

10. B Waves approach A A+B Waves occupy same space Waves diverge A B

11. Destructive Interference Waves approach A B Waves occupy same space A+B Waves diverge A B

12. This concept of adding the amplitudes of waves is known as the superposition principle.It states that at any point the resulting amplitude of two interfering waves is the algebraic sum of the displacements of the individual amplitudes. Homework: Superposition worksheet p. 222 1-3 (just sketch)

13. Waves approach each other Overlap Resulting Wave Pattern Remember this pattern only appears for an instant!

14. 6.7 Mechanical Resonance Resonance is the response of an object that is free to vibrate to a periodic force with the same frequency as the natural frequency of the object. Therefore resonance is also a transfer of energy from one object to another having the same natural frequency. If the two objects are touching, it is known as mechanical resonance.

15. Every object has a natural frequency at which it will vibrate. A swing’s natural frequency will depend on the length of the chains. A window rattles with its natural frequency. Bridges, propellers, blades, turbines, glasses and many types of equipment all have a natural frequency. Read p. 223-224 for examples.

16. If you push someone on a swing at the right time they will travel higher and higher on a swing (with the swing’s natural frequency). When an object vibrates in resonance with another, it is called a sympathetic vibration.

17. Standing Waves – A Special Case of 1 Dimensional Wave Interference The amplitude and the wavelength of interfering waves are often different. However if the conditions are such that two waves have the same amplitude and wavelength and travel in opposite directions, then a special interference pattern known as a standing wave occurs.

18. The resulting wave pattern is known as the standing wave interference pattern. Node (N): point that remains at rest Antinode: point midway between nodes where maximum constructive interference occurs N N N N λ 2

20. The distance between two successive nodes in a vibrating string is 10cm. The frequency of the source is 30 Hz. What is the speed of the waves? f = 30 Hz λ = ? v = ? Distance between successive nodes is ½ λ ½ λ = 10 cm λ = 20 cm Hwk: p.229 1-4 v = f λ v = (30 Hz)(0.20m) v = 6.0 m/s