The speed of a wave in simple harmonic motion on a string is defined by the equation $$v= \sqrt{\frac{F}{\mu}}$$, where "v" represents the horizontal velocity of the wave, "F" is the tension force in the string, and "μ" is the linear mass density. The tension force can be approximated as acting in the horizontal direction, and the difference between horizontal tension and resultant tension is negligible for small vertical displacements. This approximation allows for a simplified analysis of wave speed without significant loss of accuracy.
PREREQUISITESPhysics students, educators, and anyone interested in understanding wave dynamics in strings, particularly in the context of simple harmonic motion and musical acoustics.
That "F" is the Tension force:annamal said:
Yes, I know that F is the tension but is F the tension of the string in the x direction or is F the tension that is tangent to the string.berkeman said:
It does not matter. To the approximation that is used to derive the wave equation, the difference is negligible.annamal said:
Yes, this makes the tension of the string in the horizontal direction as wellJT Smith said:
Ok, not sure how the tension in the x direction can be approximated as the resultant tensionOrodruin said:
The vertical displacement amplitude is assumed to be small in those derivations, so the tension in the string is not affected (in magnitude) by the wave passing by. Does that help?annamal said: