A sinusoidal transverse wave reaches a perfectly free end of a string located at x = 0. The incident wave is yᵢ = A cos(kx-ωt). Which expression correctly represents the reflected displacement wave?
Options

Question

A sinusoidal transverse wave reaches a perfectly free end of a string located at x = 0. The incident wave is yᵢ = A cos(kx-ωt). Which expression correctly represents the reflected displacement wave?

Options

G1 Physics · Accepted Answer

At a free end, the transverse force must vanish. For a stretched string this requires ∂y/∂x = 0 at the free end. A reflected wave travelling in the −x direction with no phase reversal is yᵣ = A cos(kx+ωt). At x = 0, the derivatives of the incident and reflected waves cancel, satisfying the free-end condition. Thus there is no phase reversal of displacement at a perfectly free end. Correct option: B.

A sinusoidal transverse wave reaches a perfectly free end of a string located at x = 0. The incident wave is yᵢ = A cos(kx−ωt). Which expression correctly represents the reflected displacement wave?