A sinusoidal transverse wave travels along a string towards a perfectly fixed end located at x = 0. Near the end, the incident wave is represented by yᵢ = A cos(kx-ωt). The origin is chosen at the reflecting end. Which expression correctly represents the reflected displacement wave?
Options

Question

A sinusoidal transverse wave travels along a string towards a perfectly fixed end located at x = 0. Near the end, the incident wave is represented by yᵢ = A cos(kx-ωt). The origin is chosen at the reflecting end. Which expression correctly represents the reflected displacement wave?

Options

G1 Physics · Accepted Answer

At a perfectly fixed end, the transverse displacement must remain zero at every instant. Therefore, yᵢ(0,t)+yᵣ(0,t) = 0. Now, yᵢ(0,t) = A cosωt. Hence the reflected displacement at the boundary must be yᵣ(0,t) = −A cosωt. A reflected wave must travel in the −x direction, so its phase contains kx+ωt. Therefore, yᵣ = −A cos(kx+ωt). The minus sign is equivalent to a phase change of π on reflection. Correct option: B.

A sinusoidal transverse wave travels along a string towards a perfectly fixed end located at x = 0. Near the end, the incident wave is represented by yᵢ = A cos(kx−ωt). The origin is chosen at the reflecting end. Which expression correctly represents the reflected displacement wave?