ho_traveling_waves - Displacement of Functions The top plot...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Displacement of Functions: The top plot shows a function f ( x ) which peaks when its argument ( x ) equals b . In the bottom plot, I’ve plotted the same function f , but now every occurance of the the variable x has been replaced with the quantity x - a . Since the structure of f hasn’t changed, it must still peak when its argument is equal to b , hence the shape of f is preserved in the bottom plot but its location is displaced an amount + a along the x axis. QUESTION: What would f ( x + 2 b ) look like?
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Traveling Pulses: Suppose we wanted to make the pulse represented by function f move in the positive x direction with a speed v x . How would we write that? Simple! You just make the shift a change with time. Let a = v x t + a 0 , where a 0 is a constant used to get the position of f at t = 0 correct. Then f ( x, t ) = f ( x - v x t - a 0 ) describes a pulse with the shape f ( x ) moving in the positive x direction. QUESTION: How would the equation for a pulse traveling in the - x direction differ? Traveling Waves:
Background image of page 2
Consider the function f ( x ) = A cos( kx ). A is the amplitude, and k is called the wave number . Think of k as the conversion between distance and phase: k =
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 5

ho_traveling_waves - Displacement of Functions The top plot...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online