# Are there two ways of representing a wave travelling towards positive $x$-direction?

My textbook says

"Consider an open organ pipe of length $L$ lying along $x$-axis with its ends at $x=0$ and $x=L$. The sound wave travelling along the pipe can be represented as $\Delta P=\Delta P^0\sin(kx-wt)$."

But I've always used a "$\sin(wt-kx)$" type wavefunction to represent a wave travelling in $+x$-direction. As I know that when the coefficient of $x$ in the wavefunction is negative, it represents a wave travelling towards $+x$-direction and the opposite when there's a — in the coefficient of $x$.

So my doubt is:

Whether both the aforementioned wavefunction can be used to represent a wave travelling towards $+x$-direction or not. If yes then please explain how.

As $$\sin(kx-\omega t)=- \sin(\omega t-kx)$$ the only difference between the waves is the sign of the amplitude coefficient. Both travel to the right if $k$ and $\omega$ are positive numbers. In general the wave velocity (counted as positive if to the right) is $v_{\rm phase}= \omega/k$
• @user50973. You make the wavenumber $k$ negative to get a leftgoing wave. It's not true that $k$ has to be a positive number. – mike stone Dec 26 '17 at 17:30