A triangular wave pulse travels in the positive x-direction with speed v on a taut string of tension F and linear mass density mu. At t = 0, the pulse shape is: y = 0 for x

Question

A triangular wave pulse travels in the positive x-direction with speed v on a taut string of tension F and linear mass density mu. At t = 0, the pulse shape is: y = 0 for x < -L; y = h*(L+x)/L for -L < x < 0; y = h*(L-x)/L for 0 < x < L; y = 0 for x > L. Identify the INCORRECT statement(s) about the instantaneous power.

Accepted Answer

The magnitude of instantaneous power is zero for -L < (x - vt) < 0. For a transverse wave, the instantaneous power transmitted is P = F*v*(dy/dx)². The slope dy/dx equals +h/L in the rising region (-L < x-vt < 0), equals -h/L in the falling region (0 < x-vt < L), and is zero outside the pulse. Therefore: In region -L < (x-vt) < 0: slope = h/L, power = F*v*(h/L)² (not zero, so option A is INCORRECT). In region (x-vt) < -L: slope = 0, power = 0 (option B claims F*v*(h/L)², which is INCORRECT). In region (x-vt) > L: slope = 0, power = 0 (option C claims F*v*(h/L)², which is INCORRECT). In region 0 < (x-vt) < L: slope = -h/L, power = F*v*(h/L)² (option D is CORRECT). Incorrect statements: A, B,

Solution

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