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Nodes and Antinodes

  • Thread starter lha08
  • Start date
  • #1
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Homework Statement


Consider the standing wave: 0.005sin(30x)cos(420t) m. Locate the antinode closest to x=0.25 m.

Homework Equations





The Attempt at a Solution


I'm not really sure how to tackle this problem except that i know that antinodes occur at the crests of the standing wave and that the distance between antinodes is lamda/2. In the answers it says that: kXn=(2n+1)pi/2..... Xn=(2n+1)pi/(2k) and when you plug in n=2 it is 0.261 m...does anyone know how they got the initial formula?

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Doc Al
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Consider the spatial factor sin(kx). What values of x give the maximum amplitude?
 
  • #3
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Consider the spatial factor sin(kx). What values of x give the maximum amplitude?
aren't they pi/2, 3pi/2, 5pi/2, 7pi/2...etc?
 
  • #4
Doc Al
Mentor
44,882
1,129
aren't they pi/2, 3pi/2, 5pi/2, 7pi/2...etc?
Good. But that's the value for kx, not x. (In this problem, k = 30.) How would you write that series using n, where n = 0, 1, 2, and so on? Compare that to the formula given.
 

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