MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 11
        Please give the derivation of the equation of wave motion
8 years ago

Answers : (1)

SAGAR SINGH - IIT DELHI
879 Points
							

Dear student,

 

{ \partial^2 u \over \partial t^2 } = c^2 \nabla^2 u

where \scriptstyle\nabla^2 is the (spatial) Laplacian and where c is a fixed constant equal to the propagation speed of the wave. This is known as the non-dispersive wave equation. For a sound wave in air at 20°C this constant is about 343 m/s . For the vibration of a string the speed can vary widely, depending upon the linear density of the string and the tension on it. For a spiral spring  it can be as slow as a meter per second. More realistic differential equations for waves allow for the speed of wave propagation to vary with the frequency of the wave, a phenomenon known as dispersion.

v_\mathrm{p} = \frac{\omega}{k}.

Another common correction in realistic systems is that the speed can also depend on the amplitude of the wave, leading to a nonlinear wave equation:

{ \partial^2 u \over \partial t^2 } = c(u)^2 \nabla^2 u
8 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 101 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 110 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details