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A uniform cord of constant density and length L, and with total mass m is hung vertically and freely from a support as shown in diagram. (a) What is
A uniform cord of constant density and length L, and with total mass m is hung vertically and freely from a support as shown in diagram.
(a) What is the linear density of the cord?
(b) The tension of the cord is not a constant. Write down the tension of the cord as a function of h. Note that the tension is zero at the very bottom of the cord.
(c) Using results from (a) and (b), calculate the speed of the transverse waves in this cord.
(d) Using result from (c), calculate the time it takes for a pulse to travel upward from the bottom end to the top end? Note that since the speed is not a constant, one needs to integrate the differential time for the wave that travels a differential length of dh.
