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Posted by on Sunday, August 5, 2012 at 9:31pm.

Standing waves on a string are generated by oscillations having amplitude 0.005 m, angular frequency 942 rad/s, and wave number 0.750p rad/m.

a.) What is the equation of the standing wave?
b.) At what distances from x=0 are the nodes and antinodes?
c.) What is the frequency of a point on the string at an antinode?
d.) If the string is 4m long, how many nodes are there?

  • physics - , Monday, August 6, 2012 at 10:10am

    y(x,t) =|2•A•coskx|•cosωt,
    y(x,t) =|2•0.005•cos(0.750•π•x)| •cos(942•t),
    Antinods:
    x=m• (λ/2), m=0,1,2,...
    The 1st antinode at the origin (m=0),
    the 2nd antinode at λ/2 (m=1).
    Distance from origin = λ/2
    Nodes:
    x= (m+½)• (λ/2).
    The 1st node at λ/4 (m=0),
    the 2nd antinode at 3λ/4 (m=1)
    Distance from origin = λ
    The frequency is f=ω/2π=942/2 π =149.9 Hz.
    λ=2π/k=2π/0.75 π=8/3 (meters).
    If the antinode is at the origin, then we have
    3 nodes on the distance 4 m at the points:
    x=λ/4, 3λ/4, 5λ/4,
    and 4 antinodes at
    x= 0, λ/2, λ, 3λ/2.

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