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124. Problem 19.23 (RHK) A non-uniform wire of length L and mass M has a variable
linear mass density given by
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,
where x is the distance from one end of the wire and k is a constant. We have to
show (a) that
. (b)
We have to show that the time t required for a pulse generated at one end of the
wire to travel to the other end is given by
, where F is the tension in the wire.|
Solution: Click For PDF Version (a) Mass density of the wire is
(b) Speed of wave motion in the wire will be a function of position x as mass density varies with x. As the wire is under uniform tension F, we have
Therefore, the time t required by a wave pulse generated at one end to travel to the other end of the wire will be
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