Answer:
W = 0.135 N
Explanation:
Given:
 - y (x, t) = 8.50*cos(172*x -2730*t)
 - Weight of string m*g = 0.0126 N
 - Attached weight = W
Find:
The attached weight W given that Tension and W are equal.
Solution:
The general form of standing mechanical waves is given by:
                             y (x, t) = A*cos(k*x -w*t)  
Where k = stiffness and w = angular frequency 
Hence,
                            k = 172 and w = 2730
- Calculate wave speed V:
                             V = w / k = 2730 / 172 = 13.78 m/s
- Tension in the string T:
                             T = Y*V^2
where Y: is the mass per unit length of the string.
 - The tension T and weight attached W are equal:
                            T = W = Y*V^2 = (w/L*g)*V^2
                             W = (0.0126 / 1.8*9.81)*(13.78)^2
                             W = 0.135 N