**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**