Mathematics OpenStudy (anonymous):

Why does the wave equation involve second partial derivatives? If it were $\frac{\partial f}{\partial x} = \frac{1}{v}\frac{\partial f}{\partial t},$ would it yield the same set of solutions $$f$$ as the standard wave equation? OpenStudy (anonymous):

Take a sample wave equation and try the derivation yourself OpenStudy (anonymous):

f=Ae^(i(kx-wt)) OpenStudy (anonymous):

The subtlety of my question is more whether the formulation I wrote admits more solutions than the standard wave equation. OpenStudy (anonymous):

Of course...solutions to PDEs come in families dont they..in effect any linear combinations of valid solutions would satisfy this OpenStudy (anonymous):

I realize this. I don't think you understand my equation thoroughly. In clearer terms, does $\frac{\partial f}{\partial x} = \frac{1}{v}\frac{\partial f}{\partial t},$ which is my wave equation, have any solutions $$f(x,t)$$ that does not satisfy$\frac{\partial^2 f}{\partial x^2} = \frac{1}{v^2}\frac{\partial^2 f}{\partial t^2},$ which is the standard wave equation? OpenStudy (anonymous):

I dont know much...but I guess there must be...becz the second eqn imposes one more condition..not sure OpenStudy (vincent-lyon.fr):

@yakeyglee: wow, this is a good question! Did you come up with this yourself, or did your teacher point at it? Now, here's my contribution: Answer to your question is: this equation has fewer solutions than the wave equation. Here are two examples: f(x,t) = A cos [ω(t - x/v)] is solution of wave equation, but not of your first order equation. Try it! f(x,t) = A cos(ωt).cos(ωx/v) has same properties. Ok, I'll let you digest this: I hope it will lead you to more questioning, because it is not the end of it. OpenStudy (anonymous):

This was my own question. And interesting...I see that allows for the translation of waves in both directions. What if we limited ourselves to waves that only propagated in the negative direction? Would the solutions be different then? OpenStudy (vincent-lyon.fr):

Exactly, what you got is only one set of solution of the wave equation, namely "travelling waves in -x direction". But travelling waves in +x direction and standing waves, are also solutions of the (full) wave equation.

Latest Questions RabbitLovely: Please help I don't have any in my family Choose one story from your oral tradition and re-tell it in short story or poem form.
1 minute ago 0 Replies 0 Medals troyboy380: The set of ordered pairs (u20131, 8), (0, 3), (1, u20132), and (2, u20137) represent a function.
4 minutes ago 0 Replies 0 Medals patrickf220: Walt Whitman revised Leaves of Grass many times. Which of the following statements are true about the various editions? Select all that apply.
22 minutes ago 0 Replies 0 Medals Kayjo772: dude's family is exchanging Euros for US Dollars the exchange rate is u20ac1 equal 1.
22 minutes ago 0 Replies 0 Medals giselle: Dale draws a line in place of his pencil and folds the grid paper along the line. How do the triangles align when the grid paper is folded? Explain
24 minutes ago 0 Replies 0 Medals Noodlearms: In which different ways can 45 be written as the product of two positive integers? Choose all answers that are correct.
32 minutes ago 0 Replies 0 Medals Brazzyxy: A character faces a conflict because the community rejects her. What kind of conf
30 minutes ago 1 Reply 0 Medals beth55355: Rewrite the sentence to make the pronoun reference clear. She traced her ancestry back to the original president of the college, which her roommate thought
31 minutes ago 2 Replies 0 Medals Acolgrove: who is the most active qeastion cove user
26 minutes ago 25 Replies 0 Medals alexisHales: Which type of resource are newspaper accounts written at the time an event occurr
48 minutes ago 0 Replies 0 Medals