Creating Wave Functions With One Variable: Can It Be Done?

[johann1301]

With the number i, its possible to create a wave function with just one variable.

example:

f(x)=i^x

or..

f(x)=2^ix

But is there any wave function without the number i AND with only one(x and y) variable? can this be created?

 

[ckaspereli]

y = sin(x)

 

[emailanmol]

Hello,

Are you aware of the general equation of a wave?

Hint: (It is a second order differential equation)

 

[chiro]

With the number i, its possible to create a wave function with just one variable.

example:

f(x)=i^x

or..

f(x)=2^ix

But is there any wave function without the number i AND with only one(x and y) variable? can this be created?

If you want something that oscillates, then something of the form r(x)e^(ig(x)) will give you that. A standard linear wave will be in the form g(x) = wx + c corresponding to a shift and frequency information and if you want a 'real' waveform with the same peak and trough for every wavefront then r(x) = c.

This expression will give you a complex wave-form with a real and imaginary component and if you want one or the other and not both you need to use the normal identities to get rid of the i term or the real term.

 

[HallsofIvy]

In fact, it is possible to construct a one-dimensional wave of any shape.

 

[johann1301]

y = sin(x)

This is the same as

y=1/2 i e^(-i x)-1/2 i e^(i x)

so that would be "cheating"...

 

[johann1301]

(ig(x))

does this mean i*g(x) (the imaginary unit times the function g of x)?

 

[johann1301]

Hello,

Are you aware of the general equation of a wave?

Hint: (It is a second order differential equation)

I don't know anything about differential equations:(