1. WAVE MOTION

2. WAVE MOTION It is define as the disturbance travelling
In a medium,due to vibratory motion of
the medium by virtue of elasticity and
Inertia.

3. Types of waves
Transverse waves.
Longitudnal waves.

6. Wave Equation in 1d u(x, t) = ? Boundary Conditions:l u
u(x, t) = ?
Boundary Conditions:
Initial Conditions:

7. Impedance matching Wave of zero amplitude Lots of examples
2 common approaches to reduce reflection:
l/4 coupler
examples: anti-reflection coatings on lenses.
Destructive interference of the reflected waves gives a total reflected wave of zero amplitude.
Energy conservation gives 100% transmission.
Conditions for destructive interference:
same amplitude, |Yr| =|Yrtr|, (gives the same reflection coefficient at each surface)
out-of-phase by l/2. i.e. l = l/4 (hence name).
Note: for an optical system l = l/4 is chosen in the middle of the visible spectrum. Hence the “purple” bloom on coated lenses.
Wave of zero amplitude

8. Impedance matching, continued..
Gradual impedance changes
change impedance over a distance >> l.
infinitesimal reflections at each infinitesimal change in impedance.
Lots of small reflections with a large range of phase give a small net resultant reflected wave.
Thus, most energy is transmitted.
Examples:
Bell on trumpet or horn.
Microwave horn
…etc….

10. Phase Velocity for a massive particle and massless Particle
phase velocity does not describe particle motion

11. Group Velocity=Particle velocity

12. Group Velocity=Particle velocity.

13. Relation Between Group Velocity and Phase Velocity

15. This gives us the relation between Phase velocity and Group velocity

16. THANK YOU.