1. Basic properties of waves One-dimensional wave t=0 t circular wave-number wave-number angular frequency frequency phase speed phase measures the position of a wave feature, such as a wave peak or trough wavelength distance between repeating units of a propagating wave period T duration of one cycle in a repeating event number of occurrences of a repeating event per unit time

2. Euler formula i: imaginary unit Harmonic wave : one amplitude and one frequency Waves superimpose together Example 1: standing wave Right moving wave Left moving wave

3. Example 2: Non-dispersive and dispersive wave Specific case 1 Non-dispersive wave-packet Specific case 2 Dispersive wave-packet Non-dispersive wave: wave phase speed dos not depend on wave number. Dispersive wave: wave phase speed depends on wave number.

4. Specific case 3 Specific case 4 Because of the reinforcement or cancellation of wave amplitude, the energy of wave group will be concentrated in regions where the wave amplitude is large, and those regions with small wave amplitude contain less energy. Thus, wave energy does not propagate at the phase speed of individual waves, but at the speed of wave envelope, called group velocity.

5. Group velocity high frequency carrier wave slow moving envelope wave group velocity

7. Longitudinal wave: parcel's oscillation is in the same direction as the direction of wave propagation. Transverse wave: parcel's oscillation is perpendicular to the direction of wave propagation. Orbital wave: involving components of both longitudinal and transverse wave.

8. X direction acoustic wave Momentum equation Mass conservation equation Energy conservation equation Non-dispersive wave Adiabatic sound speed Doppler effect Sound frequency

9. Stationary sound source

10. Sound source moving at a speed slower than sound speed Sound source is moving at the same speed as the sound speed This pressure wall is called shock wave

11. supersonic sound speed barrier Wave front

12. sound source moving faster than sound speed so-called Mach cone 2.45 c