Why Do Wave Equations Use Sinθ and Cosθ Interchangeably?

[Saxby]

Why do some wave equations use sinθ and others cosθ?

Does it make a difference when calculating properties such as wavelength and wave number?

For example:
y(x,t) = Asin(ωt+kx)
y(x,t) = Acos(ωt+kx)

 

[sankalpmittal]

Why do some wave equations use sinθ and others cosθ?

Does it make a difference when calculating properties such as wavelength and wave number?

For example:
y(x,t) = Asin(ωt+kx)
y(x,t) = Acos(ωt+kx)

These are the equations of transverse progressive waves. They have sin or cos because they are harmonic in nature. Yes of course if you do not write the equation in form of harmonic functions will they really remain harmonic ? Not at all !

I am sure your textbook might be answering questions better than me.

Edit: CompuChip beat me to it! Saxby, I did not see your question clearly. Of course, whether you use sin or cos in harmonic function is your own choice. Cos is just shifted by phase difference of pi/2. Also it does not matter because you can set your own origin anywhere in space...

 

[CompuChip]

They are the same, the cosine is just a sine offset by $\pi / 2$:
$$\cos(x) = \sin(x + \pi / 2)$$

The most general form would be
$$y(x, t) = A \sin(\omega t + k x + \phi)$$
where $\phi$ is some initial phase that determines y(0, 0).
Usually, however, problems are (or can be) setup such that y(0, 0) = 0 or y(0, 0) = A.

 

[Saxby]

Thanks for your help guys :)