Question Detail
Question
A wave of frequency 300 Hz travels at a velocity of 250 m/s. What is the distance between two points on the wave that are 30° out of phase?
Correct Answer
Option A is the correct answer.
Detailed Explanation
The phase difference (Δφ) is related to the distance (Δx) by Δφ = kΔx, where k is the wave number. The wave number k can be found using k = ω/v = 2πf/v.First, convert the phase difference from degrees to radians: 30° = π/6 radians.Calculate k: k = (2π * 300 Hz) / 250 m/s = 600π / 250 = 12π/5 rad/m.Now, find Δx: Δx = Δφ / k = (π/6) / (12π/5) = (π/6) * (5/12π) = 5 / 72 m.5/72 m ≈ 0.0694 m.
Hint
Recall the relationship between phase difference, wave number, and distance. Also, convert degrees to radians.