Home
Class 12
PHYSICS
Show that the wave funcation y = e^(b(x-...

Show that the wave funcation `y = e^(b(x-vt))` is a solution of the linear wave equation.

Text Solution

Verified by Experts

`Y = e^(b(x-vt)) , (dely)/(delt) = be^(b(x-vt))` and `(dely)/(delt) = (bv)e^(b(x-vt))`
`(del^(2)y)/(delx^(2)) = b^(2)e^(b(x-vt))` and `(del^(2)y)/(delt^(2)) = (bv)^(2)e^(b(x-vt))`
obviously , `(del^(2)y)/(delx^(2)) = (1)/(v^(2))(del^(2)y)/(delt^(2))` which is a Linear wave equation.
Promotional Banner

Topper's Solved these Questions

  • WAVE ON STRING

    RESONANCE ENGLISH|Exercise Board Level Exercise|27 Videos

  • WAVE ON STRING

    RESONANCE ENGLISH|Exercise Exercise- 1 PART I|23 Videos

  • WAVE ON STRING

    RESONANCE ENGLISH|Exercise Exercise- 3 PART II|7 Videos

  • TRAVELLING WAVES

    RESONANCE ENGLISH|Exercise Exercise- 3 PART I|19 Videos

  • WAVE OPTICS

    RESONANCE ENGLISH|Exercise Advanced Level Problems|8 Videos

Similar Questions

Explore conceptually related problems

Verify that wave function (y=(2)/(x-3t)^(2)+1) is a solution to the linear wave equation, x and y are in centimetres.

x=5 and y=2 is a solution of the linear equation

Show that x y=a e^x+b e^(-x)+x^2 is a solution of the differential equation x(d^2y)/(dx^2)+2dy/dx-x y+x^2-2=0.

Show that y=a e^(2x)+b e^(-x) is a solution of the differential equation (d^2y)/(dx^2)-((dy)/(dx))-2y=0.

Check whether the following equation is a solution to one dimensional wave equation. y-4x-7t

Show that \ y=A e^(B x) is as solution of the differential equation (d^2y)/(dx^2)=1/y((dy)/(dx))^2dot

Show that y=a*e^(2x)+b*e^(-x) is a solution of the differential equation (d^(2)y)/(dx^(2))-(dy)/(dx)-2y=0 .

Show that y=b e^x+c e^(2x)\ is a solution of the differential equation (d^2y)/(dx^2)-3(dy)/(dx)+2y=0.

In the wave equation, y = Asin(2pi)/(a)(x-bt)

Show that y=c*e^(-x) is a solution of differential equation (dy)/(dx)+y=0 .