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Standing wave question

  • Thread starter vivekfan
  • Start date
  • #1
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Homework Statement



If a standing wave is produced by two identical waves travelling 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!
 

Answers and Replies

  • #2
181
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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?
 
  • #3
34
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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?
 
  • #4
181
0
Does that mean that the standing wave has the same wavelength as the original?
I think so.
Try drawing some pictures.
 

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