Let F(x, y, t) be a function of three independent variables. If F(x,y,t) = sin(kx) sin(ky)...

Transcribed Image Text:

Let F(x, y, t) be a function of three independent variables. If F(x,y,t) = sin(kx) sin(ky) sin[vt(k + k)/], where k, k2, and v are constants, show that F(x, y, t) satisfies the equation 8 F t 8 F v2 == 12 a F + Dy2 (1) (2) All the quantities are symbols so far. If x and y represent the position on a 2D plane, and t represents the time, what are the units of k, k2, and v and v(k + k) 1/2? Let F(x, y, t) be a function of three independent variables. If F(x,y,t) = sin(kx) sin(ky) sin[vt(k + k)/], where k, k2, and v are constants, show that F(x, y, t) satisfies the equation 8 F t 8 F v2 == 12 a F + Dy2 (1) (2) All the quantities are symbols so far. If x and y represent the position on a 2D plane, and t represents the time, what are the units of k, k2, and v and v(k + k) 1/2?