What is the phase difference between two points on a wave that are 1/4 of a wave

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Question: What is the phase difference between two points on a wave that are 1/4 of a wavelength apart? (2021)

Options:

Correct Answer: π/2 rad

Exam Year: 2021

Solution:

The phase difference Δφ is given by Δφ = (2π/λ) * Δx. For Δx = λ/4, Δφ = (2π/λ) * (λ/4) = π/2 rad.

What is the phase difference between two points on a wave that are 1/4 of a wavelength apart? (2021)

What is the phase difference between two points on a wave that are 1/4 of a wavelength apart? (2021)

Step 1: Understand that a wave has a wavelength (λ), which is the distance between two consecutive points that are in phase.
Step 2: Recognize that the phase difference (Δφ) between two points on a wave can be calculated using the formula Δφ = (2π/λ) * Δx, where Δx is the distance between the two points.
Step 3: Identify that in this question, the two points are 1/4 of a wavelength apart, so Δx = λ/4.
Step 4: Substitute Δx into the formula: Δφ = (2π/λ) * (λ/4).
Step 5: Simplify the equation: Δφ = (2π/λ) * (λ/4) = (2π/4) = π/2.
Step 6: Conclude that the phase difference between the two points is π/2 radians.

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