Question Detail
Question
A wave on a string is described by y = 2cos(0.02x – 28t – 0.7). Assuming this wave can form a standing wave through reflection, what is the distance between consecutive nodes and antinodes in the resulting standing wave?
Correct Answer
Option A is the correct answer.
Detailed Explanation
From the given traveling wave equation y = A cos(kx - ωt - φ), we can identify the wave number k = 0.02 rad/m.The wavelength λ is given by λ = 2π/k = 2π / 0.02 = 100π m.In a standing wave, the distance between consecutive nodes is λ/2, and the distance between consecutive antinodes is also λ/2. The distance between a consecutive node and an antinode is λ/4.Therefore, the distance between consecutive nodes and antinodes = 100π / 4 = 25π m.
Hint
Identify the wave number 'k' from the given equation. Use it to find the wavelength (λ). Remember the spatial relationships of nodes and antinodes in a standing wave.