A wave is represented by the equation y(x,t) = 3.2 cm sin(1000 rad/s t - 50 m^-1 x).Another wave is represented by the equation y(x,t) = 4.2 cm sin(1000 rad/s t - 50 m^-1 x).If the two waves interfere destructively,then what is equation that represents the coherent superposition of the two waves? A) y(x,t)= 7.4 cm sin(1000 rad/s t + 50.0 m^-1 x) B) y(x,t)= 1.0 cm sin(1000 rad/s t - 50.0 m^-1 x) C) y(x,t)= 1.0 cm sin(1000 rad/s t + 50.0 m^-1 x) D) y(x,t)= 7.4 cm sin(1000 rad/s t - 50.0 m^-1 x)

Question

Quizplus · Accepted Answer

When two waves interfere destructively, the amplitude of the resulting wave is the difference between the amplitudes of the two waves. In this case, the amplitudes are 3.2 cm and 4.2 cm, so the amplitude of the resulting wave is 4.2 cm - 3.2 cm = 1.0 cm. The equation for the resulting wave can be found by adding the equations for the two waves and using the amplitude of the resulting wave: y(x,t) = (3.2 cm sin(1000 rad/s t - 50 m^-1 x)) + (4.2 cm sin(1000 rad/s t - 50 m^-1 x)) y(x,t) = 7.4 cm sin(1000 rad/s t - 50 m^-1 x) So the best choice is (B), y(x,t)= 1.0 cm sin(1000 rad/s t - 50.0 m^-1 x).

A Wave Is Represented by the Equation Y(x,t) = 3