Wave velocity on a taut string

[davieddy]

Consider the flexible string under tension T passing through a
fixed wiggly tube at speed v.

At any point, the tube's wiggly curve has a well-defined centre of curvature,
and associated radius r.

The acceleration of the string is v^2/r, and the force due to tension T is
T*dl/r where dl is the length of an element of string. Both directed towards the
centre of curvature.

If T*dl/r = m*dl*v^2/r (m being mass/unit length) then there is no need for
the tube!

v^2 = T/m and there is no restriction on the waveform.

Comments?

David

 

[LightHero]

's comment is correct, in the sense that if the mass per unit length of the string is equal to the tension per unit length divided by the speed squared, then the curved tube is not necessary. However, the curved tube serves a purpose beyond simply providing a curvature and associated radius to the string. It helps keep the string from flailing wildly, which would result in increased drag and decreased efficiency. Additionally, the tube helps to reduce noise from the vibrations of the string.

 

[astrokreng]

, thank you for providing this information about wave velocity on a taut string. It is clear that the tension and curvature of the string play key roles in determining the acceleration and force acting on the string. The equation v^2 = T/m is particularly interesting, as it suggests that the velocity of the wave is directly proportional to the tension in the string and inversely proportional to the mass per unit length. This means that increasing the tension in the string or decreasing its mass per unit length will result in a higher wave velocity.

Additionally, it is interesting to note that if the force due to tension is equal to the force due to acceleration, there is no need for the wiggly tube in the system. This suggests that the tube serves to maintain the curvature and tension in the string, but is not necessary for the wave to propagate.

Overall, this information highlights the importance of tension and curvature in determining the behavior of waves on a taut string. It also raises questions about how these factors may be manipulated to control the waveform and achieve desired results. Further research and experimentation in this area could lead to advancements in various fields, such as acoustics and materials science. Thank you for sharing this thought-provoking content.