How Can Wave Speed Remain Constant When Particles Move at Different Speeds?

[gandharva_23]

when we say that speed of a wave is u we mean that with respect to the medium the wave is traveling with a speed u . now consider a sine wave traveling in positive X direction on a string . all the particles of string (these are particles of medium ) will have different speeds . The wave has the same speed wrt all these particles and its speed is u (constant) . how is this possible ?

let us say that a wave wave is propagating along +x axis with a speed u . all the particles have different speeds (along y-axis wrt ground ) . let us say a particle p1 has a speed v1j (wrt ground); wave speed wrt this particle is ui which implies speed of wave wrt ground will be ui + v1j . another particle p2 has a speed v2j (wrt ground); wave speed wrt this particle is again ui which implies speed of wave wrt ground will be ui + v2j . this implies wave speed wrt ground will keep on changing ... am i right ?

 

[Tide]

The average velocity of every element of string is 0. That's your reference frame.

 

[gandharva_23]

i did not understand what tide said

 

[Tide]

this implies wave speed wrt ground will keep on changing ... am i right ?

The direct answer to your original question is "No, you are wrong."

The wave speed is not the speed of the individual "particles of the medium." You measure the speed of the wave with respect to the undisturbed or mean properties of the medium.

 

[gandharva_23]

ok thanks a lot ...