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
