All of the following are solutions to the wave equation except for
A) $y ( x , t ) = A \cos [ k ( x - v t ) ]$
B) $y ( x , t ) = A \cos ( k x - a t )$
C) $y ( x , t ) = A \cos [ 2 \pi ( x / \lambda - f ) ]$
D) all of the first three are correct.
E) none of the first three is correct.

Question

Quizplus · Accepted Answer

All of the first three choices are solutions to the wave equation. Choice A represents a traveling wave moving in the positive x-direction, where $A$ is the amplitude, $k$ is the wave number, and $v$ is the velocity of the wave. Choice B is a general form of a wave, where $a$ can be related to the wave's velocity and frequency. Choice C represents a wave with a specific formulation in terms of wavelength $\lambda$ and frequency $f$, which also satisfies the wave equation.

All of the Following Are Solutions to the Wave Equation y(x,t)=Acos⁡[k(x−vt)]y ( x , t ) = A \cos [ k ( x - v t ) ]y(x,t)=Acos[k(x−vt)]

All of the Following Are Solutions to the Wave Equation $y ( x , t ) = A \cos [ k ( x - v t ) ]$