Phase Difference in Plane Wave · CAP 2022 #7

Physics

Problem

The graph below is showing the wavefronts of a plane wave with frequency 3 Hz travelling at speed v = 6 m/s hitting a board at an angle π/6. What is the phase difference between the waves at two points 1 m apart along the board? a) π2\frac{π}{2} b) π3\frac{π}{3} c) π4\frac{π}{4} d) π6\frac{π}{6}
Intuitive explanation

The key is recognizing that only the component of the wave parallel to the board matters for phase difference along it. First find the wavelength from λ=v/f\lambda = v/f, then use geometry to determine how the wavefronts are actually spaced along the board—the incident angle π/6 means the effective wavelength along the board is stretched. Finally, calculate phase difference as Δϕ=2πΔx/λeff\Delta \phi = 2\pi \Delta x / \lambda_{\text{eff}}.

Intuitive explanation

The key is recognizing that only the component of the wave parallel to the board matters for phase difference along it. First find the wavelength from λ=v/f\lambda = v/f, then use geometry to determine how the wavefronts are actually spaced along the board—the incident angle π/6 means the effective wavelength along the board is stretched. Finally, calculate phase difference as Δϕ=2πΔx/λeff\Delta \phi = 2\pi \Delta x / \lambda_{\text{eff}}.

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