Standing Wave Question: Wavelength of Resultant Wave with Two Opposing Waves

[vivekfan]

Homework Statement

If a standing wave is produced by two identical waves traveling in opposite directions, is the wavelength of the resultant wave simply the wavelength of the original wave?

Homework Equations

ysin(kx)cos (wt)

The Attempt at a Solution

I'm pretty sure it produces a wavelength of the original wave because A standing wave requires that the nodes and antinodes remain in the same place, but I want to make sure. Please help!

 

[davieddy]

sinA + sinB == 2sin((A+B)/2)cos((A-B)/2)

so a sin(kx - wt) + a sin(kx + wt) = 2a sin(kx)cos(wt)

k is 2pi/wavelength.

Any help?

 

[vivekfan]

sinA + sinB == 2sin((A+B)/2)cos((A-B)/2)

so a sin(kx - wt) + a sin(kx + wt) = 2a sin(kx)cos(wt)

k is 2pi/wavelength.

Any help?

Does that mean that the standing wave has the same wavelength as the original?

 

[davieddy]

Does that mean that the standing wave has the same wavelength as the original?

I think so.
Try drawing some pictures.