a pulse is generated at lower end of a hanging rope of uniform density and length L the speed of the process when it reaches the midpoint of rope is
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Let a pulse is generated at lower end of a hanging rope of uniforms density and length L .
speed of wave ,
where T is tension and is linear mass density.
Cut an element of thickness, dx , x distance from lower end of hanging rope. so, mass of rope of length x ,
now, velocity of wave at x distance from lower end ,
The speed of the process when it reaches the midpoint of the rope is v =
speed of wave ,
where T is tension and is linear mass density.
Cut an element of thickness, dx , x distance from lower end of hanging rope. so, mass of rope of length x ,
now, velocity of wave at x distance from lower end ,
The speed of the process when it reaches the midpoint of the rope is v =
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Let a pulse is generated at lower end of a hanging rope of uniforms density and length L .
speed of wave , v=\sqrt{\frac{T}{\mu}}v=
μ
T
where T is tension and \muμ is linear mass density.
Cut an element of thickness, dx , x distance from lower end of hanging rope. so, mass of rope of length x , dm=\left(\frac{mx}{l}\right)dm=(
l
mx
)
T=\left(\frac{mgx}{l}\right)T=(
l
mgx
)
now, velocity of wave at x distance from lower end , v=\sqrt{\frac{mgx/l}{m/l}}=\sqrt{gx}v=
m/l
mgx/l
=
gx
The speed of the process when it reaches the midpoint of the rope is v = \sqrt{gL/2}
gL/2
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