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egenriether
Ok, Brainly doesn't have the required math symbols I need to give you the best looking answer so we'll have to do this the best we can.  In short, yes it could be a wave.  A simple wave,ψ,  is described by the equation
d²ψ/dx² - (1/c²)d²ψ/dt² = 0.  The right side must be a nonzero constant, which is zero here.  This is a basic wave equation.  It says if the second partial derivative of a function with respect to space minus the second partial derivative of that function with respect to time, multiplied by a constant (1/c² here) equals a constant (0 here) then that function describes a wave.  Brainly doesn't have a partial derivative symbol so I used "d". Also the c in my equation is the speed of the wave.  Not necessarily the same c as in your equation.

Now let's look at your function.  The second partial derivative of it with respect to x makes the t term 0 (it's a constant as far as x is concerned) and the x term becomes 2c.  Doing the same thing for the partial derivative of it for t leaves 2d.  These terms represent two constants, which if subtracted, as the wave equation requires, would lead to a constant on the right, which could be made zero if the coefficients c and d are chosen correctly.  
Lanuel

Since the displacement D(x, t) = cx² + dt² satisfies the traveling wave equation, it is a traveling wave.

What is a traveling wave?

A traveling wave can be defined as a type of wave in which the particles within the medium of propagation are progressively moved in the same direction as the wave with a definite velocity.

Mathematically, a traveling wave is represented by this equation:

[tex]\frac{d^2D}{dt^2} =V^2 (\frac{d^2D}{dx^2} )[/tex]

Where:

V is the velocity of a wave.

In order to determine whether the given displacement is a possible traveling wave, we would take a partial derivative of D(x, t) with respect to x.

D(x, t) = cx² + dt²

[tex]\frac{dD}{dx} =2cx[/tex]

Next, we would take a second derivative:

[tex](\frac{d^2D}{dx^2} )=2c[/tex]

Similarly, we would take a partial derivative of D(x, t) w.r.t t.

D(x, t) = cx² + dt²

[tex]\frac{dD}{dt} =2dt[/tex]

Next, we would take a second derivative:

[tex](\frac{d^2D}{dt^2} )=2d[/tex]

Substituting the derivatives into the traveling wave equation:

[tex]2d =V^2 (2c)\\\\V^2=\frac{2d}{2c} \\\\V=\sqrt{\frac{d}{c}}[/tex]

Read more on traveling wave here: https://brainly.com/question/15580786

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