Amplitude of particles in progressive waves

[Krisd98]

Homework Statement

I don't understand how all the particles in a progressive wave can have the same amplitude. Surely they're all moving along the wave therefore cannot have the same amplitude.

Homework Equations

The Attempt at a Solution

 

[olivermsun]

I don't understand your statements under (1). First of all, it is not true for all progressive waves that all particle motions have the same amplitude. However, for some waves the amplitudes are the same — why would you say that they can't be?

 

[Krisd98]

I don't understand your statements under (1). First of all, it is not true for all progressive waves that all particle motions have the same amplitude. However, for some waves the amplitudes are the same — why would you say that they can't be?

in my textbook I have a table of comparisons between progressive and stationary waves. It says that in stationary waves the amplitude of the particles differs from 0 at the nodes and max at the antibodies. It then says that in progressive waves the amplitude of the particles is the same for all particles. I don't understand why all the particles have the same amplitude in a progressive wave

 

[olivermsun]

"Ideal" progressive waves have to progress (travel) along the medium, so each point along the medium is going to be "feel" the passage of each wave as it passes by. It's that cycle of motion as each wave passes by that defines the amplitude.

For a pure standing wave, which is equivalent to two equal waves progressing in opposite directions, the constructive/destructive interference between the waves works out such that at some fixed points (the nodes) there is always maximum destructive interference and hence the amplitude is zero, and at other fixed points (the antinodes) there is always maximum constructive interference and hence the amplitude is twice that of the individual waves.