18-3 Traveling waves(行波) All the waves would travel or propagate, why here say traveling waves? with respect to 'standing wave(驻波) Definition of traveling waves The waves formed and traveling in an open medium system Description of traveling waves We use a 1-D simple harmonic, transverse, plane wave as an example Mathematics expressions The vibration displacement y as a function of t and X
18-3 Traveling waves(行波) • All the waves would travel or propagate, why here say ‘traveling waves’? (with respect to ‘standing wave’(驻波)) • Definition of traveling waves: The waves formed and traveling in an open medium system. • Description of traveling waves We use a 1-D simple harmonic, transverse, plane wave as an example • Mathematics expressions The vibration displacement y as a function of t and x
The difference between vibration and wave motion Vibration y(t: displacement as a function of time Wave y(xt): displacement as a function of both time and distance 1. Equation of a sine wave 2 What we want to know y(x, 0)=ym sin( 2丌 y(x, t)=ym sin(-(x-vt) t=o t=t X vt Fig 18-6
The difference between vibration and wave motion: Vibration y(t): displacement as a function of time Wave y(x,t): displacement as a function of both time and distance ) 2 y(x,0) y sin( x m = Fig 18-6 vt y x t = 0 t = t υ What we want to know: y(x,t) = ( )) 2 y sin( x v t m − 1. Equation of a sine wave
If there is initial phase constant p in the sinusoidal waves, the general equation of the wave at time t is 2丌 y(x,D)= ym sir(-(x-v)-)(18-16) Several important concepts about waves 1) The period T of the wave is the time necessary for point at any particular x coordinate to undergo one complete cycle of transverse motion. During this time T, the wave travels a distance vT that must correspond to one wavelength n 2) The wavelength 1: the length of a complete wave shape
If there is initial phase constant in the sinusoidal waves, the general equation of the wave at time t is: ( ) ) 2 ( , ) sin( y x t = ym x − v t − (18-16) Several important concepts about waves: 1) The period T of the wave is the time necessary for point at any particular x coordinate to undergo one complete cycle of transverse motion. During this time T, the wave travels a distance that must correspond to one wavelength . vT 2) The wavelength : the length of a complete wave shape.
0°9999999999盒9息意99气 3)The frequency of the wave: f 4)The wave number:k 2丌 5)The angular frequency :o 2丌 T e18-16) y(x, t)=ym sin( kx-@t-o
3) The frequency of the wave : T f 1 = 4) The wave number: 2 k = 5) The angular frequency : f T 2 2 = = (18-16) y(x,t) = y sin( k x−t −) m
>The equation of a sine wave traveling in+x direction is y(, t)=ym sin( kx-at- (18-11 (18-16) The equation of a sine wave traveling in the -x direction is Y(x, t)=ym sin( kx+at-e)(18-12 Note that: v=nf (18-13) speed of the wave
Note that: speed of the wave ➢The equation of a sine wave traveling in direction is + x y(x,t) = y sin( k x−t −) m ➢The equation of a sine wave traveling in the direction is − x y(x,t) = y sin( k x+t −) m (18-11) (18-12) k v f = = (18-13) (18-16)