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Confusion with Standing waves

  • Thread starter jono90one
  • Start date
  • #1
28
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Homework Statement



Adjacent anti-nodes of a standing wave are 7m apart. The amplitude is 0.5m and period 0.05 seconds. Assuming the string is clamped at the position x=0m, y=0m on the left hand side.
Find the amplitude at the point 0.29 m from the right of an antinode

Homework Equations



y=ASin(ωt-kx) ? (Moving to the right, as clamped on the left?)

The Attempt at a Solution


Well at first i did
x position = λ/4 + 0.29 = (adjacent nodes are 7m apart, so λ=14) 14/4 + 0.29= 3.79m

v = λ/T = 14/0.05 = 280 m/s

hence t=d/v = 3.79/280 = 0.0135 seconds

y = ASin[(2pi/T)t-(2pi/λ)x] = 0.5sin(0)

Which I know must be wrong becuase it will be zero at a node, an that is not a node (3.5m is a node).

Im unsure what is wrong with my method though :S

Thanks.
 

Answers and Replies

  • #2
31
0
First of all the equation you've used here is for a traveling wave (as you say, it's a wave moving in the positive x direction) so it's not going to be very helpful for dealing with a standing wave.

Try adding together two waves of the same frequency and amplitude but going in opposite directions, and apply a trigonometric identity to that sum.
 

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