1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Wave speed of a transversing guitar string?

  1. Apr 10, 2010 #1
    Hi, I'm completely stuck on a homework question and I really don't even know where to start...

    A guitar string is vibrating in its fundamental mode, with nodes at each end. The length of the segment of the string that is free to vibrate is 0.382 m. The maximum transverse acceleration of a point at the middle of the segment is 9000 m/s2 and the maximum transverse velocity is 3.90 m/s.

    Part (a) asked "What is the amplitude of this standing wave?" and I was able to correctly get A=1.69×10−3m

    Now part (b) is asking "What is the wave speed for the transverse traveling waves on this string?" and I don't even know what equations to use. If someone could just point me in the right direction, tell me a useful equation, or give me a little hint, that would be great :)
  2. jcsd
  3. Apr 10, 2010 #2
    So what you probably did to solve a) was this:

    [tex] \frac{a_{max}}{v_{max}} = \omega [/tex]

    [tex] \frac{v_{max}}{\omega} = A [/tex]

    You know that [tex]v = \lambda f[/tex] or alternatively [tex]v = \frac{2\pi f}{\frac{2\pi}{\lambda}} = \frac{\omega}{k}[/tex]

    You know omega from a) and you can figure out k easily so that's what you should do for b).
  4. Apr 10, 2010 #3
    Ok, so I'm trying to work that out, but I still can't seem to get the right answer.

    So I know [tex]\omega = 9000/3.9 = 2308[/tex] and that [tex]v = \frac{\omega}{\frac{2\pi}{\lambda}}[/tex] and... I think [tex]\lambda = 4L[/tex], right? So I got 561.2, but apparently that's not right. Did I mess up with [tex]\lambda = 4L[/tex] (using 0.382 for L) or is there something else I'm missing? :confused:

    Oh, and thanks!

    Oh shoot, [tex]\lambda = 4L[/tex] is only for tubes, isn't it... Shoot. Ok, I'll keep working at it.
  5. Apr 11, 2010 #4
    Yes it's only for tubes. You need to find what the wavelength would be for a string with nodes at both ends (just draw a wave that only has two nodes).
  6. Apr 11, 2010 #5
    It was [tex]\lambda = 2L[/tex], so the answer was just 281

    Thanks for your help :biggrin:
  7. Apr 11, 2010 #6
    Yep, good job.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Wave speed transversing Date
Speed of Light waves Feb 10, 2014
One-dimensional wave equation with non-constant speed Aug 19, 2013
The Speed of a transverse wave Aug 9, 2010
Transverse Wave speed and acceleration Mar 12, 2009
Maximum speed of a transverse wave Jan 21, 2007