While performing string vibration experiments under the boundary condition that both ends are fixed, I observed that the damping of the wave is much larger when the size of the string is smaller and it decreases as the length of the string is increased.

While the string was only 9-10 cm long, under same initial conditions, the vibration lasted less than 3-4 seconds before damping out. In contrast when I increases the length to 6-7 feet the vibration continued for over 20-25 seconds.

What is the reason behind this?

  • $\begingroup$ Why do you think this effect occurs, especially if the density of the string is constant? $\endgroup$ – user163104 Aug 12 '17 at 13:28
  • $\begingroup$ Still not been able to think of a reason,it's a mere observation;any kind of help will do $\endgroup$ – user157588 Aug 12 '17 at 13:35
  • 1
    $\begingroup$ Sorry, I am being careful not to answer a homework question, the mass, and intertia will increase as the string length increases. Less damping occurs. $\endgroup$ – user163104 Aug 12 '17 at 13:42
  • $\begingroup$ Do you have any idea how to calculate the effect of air resistance? $\endgroup$ – DanielSank Jan 24 at 17:03
  • $\begingroup$ I seem to recall that (at least part of) the damping is proportionnal to the frequency. If the tensions are equal, shorter strings will vibrate at larger frequencies, hence being damped more strongly. See ccrma.stanford.edu/~jos/pasp/Frequency_Dependent_Losses.html $\endgroup$ – David Jul 9 at 10:27

The damping was also found to be inversely proportional to cable length. It seems that for certain length range damping is inversely proportional, while above a critical value the damping is independent from length, see references: Qiu, Y. (2013), ”Investigation of internal damping in carbon fiber and steel cables”, dissertation, Univ of New Mexico at Albuquerque. Yamaguchi, H., and Fujino, Yozo. (1987), “Modal damping of flexural oscillation in suspended cables”, Structural Eng. / Earthquake Eng. Vol. 4. No.2. October pp.413s-421s


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