Aug 15, 2017 · Using $\sin(kx-\omega t)$ or $\sin(\omega t-kx)$ does not make a difference: it is just a matter of convention. You can very legitimately change $A\sin(kx-\omega t)$ to $-A\sin(\omega t- kx)$ without causing any damage. Note that the full solution to the wave equation is of the form $A\sin(kx-\omega t+\phi)$.

Of course y (x,t) = sin (kx − ωt) is a graph in three dimensions, one of which is time. We can plot it in three spatial dimensions (or at least a 2D view of three dimensions). In the animation below, we combine the two views. At different times, we show a series of snapshots y (x) as grey curves, but we separate these along the graph's t axis.

若原点处是简谐振动 f(t) = A sin(\\omega t) ， 则波函数 y(x,t)=f(t-\\frac{x}{v}) = Asin(\\omega(t -\\frac{x}{v})) = A sin(\\omega t - kx) ， k = \\frac{w}{v} 。 从波函数出发我们就可以推导出波动方程的一般形式。

The book claims that the wave function of a sinusoidal wave moving in the $+x$ direction is $y(x,t) = A\cos(kx - wt)$. However, I see a drawing of the wave and they always seem to be $\cos$ graphs. Are sinusoidal waves always cosine graphs? Or can they be sine?

Whenever sin(kx - wt) is the solution to a differential equation, so will e^i(kx-wt) be. This is because in an equation, the Real part of the left hand side will always equal the Real part of the right hand side.

Feb 22, 2017 · Switching between kx-wt and wt-kx switches the sign of the amplitude if it's sine, and does nothing if it's cosine. Switching the sign of the amplitude inverts the wave, which is equivalent to a 180 degree phase shift.

\frac{\partial\varphi}{\partial k}=0\\ 决定，即波包位于相位的极值点处， \varphi=kx-wt ，其中 x，t 视为参数，对于同一时刻的同一点处，波函数大小是由许多个这样的相位叠加。

May 26, 2017 · 1) Calculate the vertical position of the string at x=0m, t=0s. 2) Calculate the phase constant, φ, of the motion. 3) Determine the vertical displacement of the string element at x=0m at time t=2s. 4) What is the speed of the wave? 1) if we let x=0m and t=0m then y=1m sin φ but how do I solve for the vertical displacement if there are two unknowns?

y=A sin (wt-kx) or y=Asin (kx-wt) ??? & -ve x-direction ??? Consider a particle O, situated at the origin. It performs a S.H.M. of amplitude A, angular frequency ω and produces a simple harmonic wave in the medium. Suppose that the wave travels in the positive direction of X-axis and the particle O starts from the mean position.

(a) The equation y = \(\alpha\) sin (wt - kx) represents a plane wave travelling in a medium along the x-direction, being the displacement at the point x at time t. (i) Given that x is in metres and t is in seconds, state the units of k and w