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a uniform mass of m and length l hangs from a celling. the speed of the transverse wave in the rope at a distance h from the lower end is ---------

a uniform mass of m and length l hangs from a celling. the speed of the transverse wave in the rope at a distance h from the lower end is ---------

Grade:12th pass

1 Answers

Arun
25750 Points
5 years ago
The speed of a transverse wave on a string is given by: 

v = sqrt(T/λ) 

where T is the tension in the string, and λ = M/L is the linear mass density of the string. 

For a string hanging vertically, mass of the rope below a point, y, on the string (measured from the bottom), is simply m(y) = y*λ = y*M/L. The weight of this portion of the string (i.e., themagnitude of the force it exerts on the end of the portion of the string above it) is g*m(y) = g*y*λ. Identifying this force as the tension in the string, we have T(y) = g*y*λ. Plugging this into the expression for the speed, we get: 

v(y) = sqrt(g*y) 
 
Hence speed will be = sqrt (g*h)
 
Hope it helps
 
Regards
Arun

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