Question Detail
Question
Two points on a travelling wave having frequency 500 Hz and velocity 300 m/s are 60° out of phase. What is the minimum distance between these two points?
Correct Answer
Option B is the correct answer.
Detailed Explanation
First, calculate the wavelength (λ) of the wave:λ = v / fGiven velocity (v) = 300 m/sGiven frequency (f) = 500 Hzλ = 300 m/s / 500 Hz = 0.6 mNext, relate the phase difference (Δφ) to the path difference (Δx):Δφ = (2π / λ) * ΔxThe phase difference is given as 60°, which is π/3 radians.π/3 = (2π / 0.6 m) * ΔxDivide both sides by π:1/3 = (2 / 0.6) * Δx1/3 = (10/3) * ΔxΔx = (1/3) * (3/10) = 1/10 = 0.1 mThe minimum distance between the two points is 0.1 m.
Hint
First find the wavelength of the wave, then use the relationship between phase difference and path difference: Δφ = (2π/λ) * Δx.