Question Detail
Question
For a standing wave described by y = 2Acos(ωt)sin(kx), the document defines nodes as points where the displacement is always zero. It specifies that for nodes, kx = nπ, where n is an integer. Given that k = 2π/λ, what are the positions of the nodes?
Correct Answer
Option B is the correct answer.
Detailed Explanation
According to page 9 of the document, nodes occur when kx = nπ, where n = 0, 1, 2, .... Substituting k = 2π/λ into this equation: (2π/λ)x = nπ. Solving for x, we get x = nπ * (λ/2π) = nλ/2. This is consistent with the 'nodes' discussion on page 9.
Hint
Substitute the expression for k in terms of λ into the condition for nodes, kx = nπ, and solve for x.