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Homework Help: Speed of Transverse Wave

  1. Apr 25, 2010 #1
    A wooden bar when struck vibrates as a transverse standing wave with three antinodes and two nodes. The lowest frequency note is 43.6 Hz, produced by a bar 55.4 cm long. Find the speed of transverse waves on the bar.


    I assumed that 3 antinodes and 2 nodes means the eigenfrequency f=3/2(v/L). I also assumed that 43.6 Hz was the fundamental frequency. Since I want f3, I multiplied 43.6 by 3 and got 130.8 Hz.

    From here I plugged into the first equation 130.8=(3/2)(v/.554) and solved for v.
    v=48.3088 m/s.

    But this answer was wrong, so I am not sure what I did wrong.

    I would appreciate any advice, Thanks,
    Jason
     
  2. jcsd
  3. Apr 25, 2010 #2
    For a wooden bar with anti-nodes on both sides, the formula for wavelength is:
    Wavelength = 2L/n, where L is the length of the bar and n is the harmonics number.

    For three antinodes and 2 nodes, the bar is in its second harmonic and so wavelength is:
    2L/2 = L

    Since Frequency*Wavelength = Velocity,
    Velocity = (43.6)(0.554) = 24.15 m/s

    **Its been a while since I did this, so i may be wrong.
     
  4. Apr 25, 2010 #3
    Thanks, that was correct.

    I guess i still don't understant how it is the second harmonic though. I thought the antinodes were the max points, and three max points means 3/2 of a wavelength. For example, two positive maximums, and one negative maximum.
     
  5. Apr 25, 2010 #4
    Ah but think about it. Say we're looking at one interval of a cosine curve (0 to 2pi). How many max points are there? How many points cross y = 0? The points that cross y = 0 are like the nodes (when you multiply the cosine curve by -1 they remain invariant) while the antinodes are the points where y = +/- 1. (This results in 3 antinodes and 2 nodes which means 3 antinodes and 2 nodes = 1 wavelength of a cosine curve).

    Its a weird way of thinking about it. But try drawing a picture, it might help.
     
  6. Apr 25, 2010 #5
    You're right, I was picturing a sine function. I didn't notice that the sine is opposite, three nodes and two antinodes.

    Thanks again
     
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