Lesson_5.3a_Printable

# Lesson_5.3a_Printable - Harmonic Waves A wave generated by...

This preview shows pages 1–6. Sign up to view the full content.

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

View Full Document

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

View Full Document

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.

Unformatted text preview: Harmonic Waves A wave generated by the simple harmonic vibrations of the particles of a medium is called a harmonic wave . What is the equation for the displacement of a simple harmonic motion? At t = 0 if the particle is at the equilibrium position, the displacement y is: y = A sin ( ϖ t) ince a harmonic wave is formed by the varying Since a harmonic wave is formed by the varying displacements of the vibrating particles, the equation for a harmonic wave is: y = A sin ( ϖ t) 2 2 T f π ϖ π = = 2 sin y A t T π = 1 A is the amplitude of the wave and f is the frequency. The displacement y can also be written as a function of x 2 sin y A t T π = v f λ = [ ] sin 2 A ft π = λ sin 2 v y A t π λ = n 2 si vt A π λ = [ ] sin y A x k = is called 2 wave number the k π λ = 2 To describe a wave advancing to the right, we replace x by x – vt where v is the wave speed. [ ] sin y x A k = The equation for a wave advancing to the right is: y = A sin[k(x – vt)] 2 ) ( sin x vt y A π λ =- 2 2 sin A t v x π π λ λ - = = A sin ( k x – 2 π f t) y = A sin (kx – ϖ t) Similarly a wave advancing to the left can be written as: y = A sin[k(x + vt)] y = A sin (kx + ϖ t) http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Fla sh/ClassMechanics/TravelWaves/TravelWaves.html 3 The wave y(x,t) = A cos k(x + 34 t) represent a traveling wave where x is in meters and t in second. What are the direction and the speed of the wave? Sine function or cosine function only determines the initial state of the wave and not the direction. Example 1 The wave y(x,t) = A sin k(x + v t) is a wave traveling to the left. The wave y(x,t) = A cos k(x + 34 t) is a wave traveling to the left with a speed equal to 34 ms-1 . 4 At time t = 0, the shape of a wave pulse on a string is given by the function: where x is in meters. Plot y(x,0) versus x and give the general wave function y(x,t) at any time t if (i) the pulse is moving in the positive x-direction with a speed of 10...
View Full Document

## This note was uploaded on 05/01/2011 for the course PHY 2048 taught by Professor George during the Fall '10 term at Edison State College.

### Page1 / 19

Lesson_5.3a_Printable - Harmonic Waves A wave generated by...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online