Meaning of Phase in stationary waves

[zorro]

What is the exact meaning of the statement " In a standing wave, all the particles are in the same phase "?

Phase, ϕ = 2(pi)x/λ
If we consider the node as origin, different particles have different x values.
Then how come the phase is same for all?

 

[K^2]

They likely mean the time-dependent factor, since the displacement in the standing wave is given by

$$sin(\omega t)sin(kx)$$

The phase of the second factor depends on position, but the phase of the first factor does not.

 

[Dadface]

What is the exact meaning of the statement " In a standing wave, all the particles are in the same phase "?

Phase, ϕ = 2(pi)x/λ
If we consider the node as origin, different particles have different x values.
Then how come the phase is same for all?

Every point in a loop(between adjacent nodes) is in phase with every other point in that loop and in antiphase with points in adjacent loops.

 

[zorro]

They likely mean the time-dependent factor, since the displacement in the standing wave is given by

$$sin(\omega t)sin(kx)$$

The phase of the second factor depends on position, but the phase of the first factor does not.

What is the difference between the two phases?

Every point in a loop(between adjacent nodes) is in phase with every other point in that loop and in antiphase with points in adjacent loops.

Please explain what's wrong in the formula I gave?

 

[Dadface]

What is the difference between the two phases?



Please explain what's wrong in the formula I gave?

Your formula gives the phase for a progressive wave

 

[Studiot]

Dadface is quite correct.

For progressive waves the term phase has two meanings.

1) You can compare the phase difference of two distinct waves as the difference in time between when each wave reaches a positive going maximum.

2) You can compare the phase difference between two points in the same wave. This is the difference in time between when each point reaches its positive going maximum.

For a standing wave all points between two successive nodes reach their positive maximum at the same time so the phase difference is zero, ie they are in phase.

 

[zorro]

Thanks!