Simple harmonic waves When a simple harmonic progressive wave is travelling through medium,then each succeeding particle lags in phase before the preceding particle.Can anyone expain how does it lag? Thanks…
 A: A wave propagates through the medium due to the interacting particles in the medium. The medium is nothing but a certain region of space containing some interacting particles. If there are only identical particles, the the medium is homogeneous. Otherwise it is heterogeneous. A wave in such a medium is nothing but a disturbance in a particle's energy in that medium. If you give some energy to the particle, it starts to vibrate. Due to interaction, this particle's vibration drags along the neighboring particles. This is how the disturbance propagates through the medium. this is what we say wave motion.  
So, the motion of a wave is determined by the medium through which it propagates. that's why the properties of a wave like the velocity are medium dependent. One particle executing vibration drags other neighboring particles and st them in vibration. This ability of a particle to transmit it's energy by vibration to another particle happens in how much time. This determines the phase lag of the particle. If the particle takes considerable time to absorb energy and then re-emit it to the neighboring particle, then the phase lag will be more. Now, as you can imagine, there will be a phase lag or no phase lag, but never will be a phase lead.
A: Let us imagine that the disturbance that causes the wave is located at position x=0. If the disturbance is oscillatory then it could be of the form $\displaystyle y(x=0,t)=A\sin\omega t$, in which y denotes the displacement of the particle of the medium, $\omega$ is the angular frequency of oscillation. The quantity $\displaystyle\omega t$ is called the phase of the vibration at x=0. The disturbance at x=0 propagates through the medium with a speed v, say. So the displacement of the particle of the medium located at x=x at time t is the displacement at x=0 at time $\displaystyle t-\frac{x}{v}$ which is $\displaystyle A\sin\omega(t-\frac{x}{v})$. Thus the phase of the vibration at x=x at time t is $\displaystyle \omega (t-\frac{x}{v})$. But the phase of the vibration at x=0 at time t is $\displaystyle\omega t$. So the phase at x=x lags the phase at x=0 by an amount $\displaystyle\frac{\omega x}{v}$.
