Understanding the Longitudinal Wave Velocity of a Helical Spring

[Kai]

v = [sqrt(D/m)] * L, where D is spring constant, m is mass of spring, L is length of the spring
My lecturer give me this formula to find the longitudinal wave velocity on an helical spring. May i know how to derive this formula?

< Mentor Note -- this is not technically a homework question, but it is okay that it is in the schoolwork forums >

 

[RedDelicious]

If you start from the general speed of wave, as derived on a string, it actually works to just substitute in the quantities for the spring into this formula. Using your notation,

$$v_c = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{DL}{M \over L}} = L\sqrt{\frac{D}{M}}$$

The transverse wave $v_t$ is different in that depends on the unstretched length $L-L_o$.

If you don't find that satisfying, you can find a simple but more convincing derivation here. The appendix on page 8 contains their full derivation of it and experimental justification.

http://netserver.aip.org/epaps/phys_teach/E-PHTEAH-46-010803/Hooke's Law Waves Online.pdf