ho_traveling_waves

# ho_traveling_waves - Displacement of Functions The top plot...

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

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?

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

View Full Document
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:
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 =

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

View Full Document
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
Ask a homework question - tutors are online