In the derivation of velocity of a wave on a string, a/c to HCV book, it is assumed that the particles move in an approximately circular path but actually the particles only move up and down a string and not sideways. How is this possible? Also the weight force is not taken into account. Please explain.

Dear student
While deriving this formula he assumed that this equation is made by the person who is moving in  the direction of wave velocity and with the same velocity as thevelocity of the wave .So he will always observe different particles of the string instead of the same particle which ofcourse move up and down but when the motion of  different particles are observed in sequence as is possible in the moving frame of the observer the combined motion of these particles constitute circular motion.Further the string is assumed to be very light.regards

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