Calculate the velocity of the transverse wave at any position

[harini_5]

a string of length l and mass m hangs freely from a fixed point
calculate the velocity of the transverse wave at any position
sol:
mass per unit length is m/l
let there be a point on the string at a distance x from free end
tension at the point=wt of the string per unit length*part of the string
=(m/l)*x*g
and sol continues.

my doubt is why isn't the upper part contributing to the tension?
weight due to upper part must be pushing down the lower part.

 

[kuruman]

If I understand your question correctly, the answer is "You can't push with a string."

 

[harini_5]

sir,
the string here has considerable mass.let us consider the part x(as i have mentionedin prob) and l-x separately.why isn't the weight due to upper part pushing down the lower part and contributing to tension?
isnt it just like a block placed over another as in this case it is clear that the upper block exerts some force over the lower?
thanks in advance.

 

[kuruman]

OK, let's consider lengths x above and L-x below. Draw a horizontal line on the string at x. The line has thickness dx and the rope at the line has mass dm = dx/L. Mass dm is in equilibrium and at rest. This means that the net force on it is zero. I know that the string of length L-x below dm exerts a force that is down because of its weight. In what direction should the string of length x above dm exert a force so that dm is at rest, down or up?