Mechanical and Standing waves Formula sheet

Mechanical and Standing waves Formula sheet - on strings...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Mechanical and Standing Waves Equation of Motion for Waves y ( x , t ) = A sin 2 " # ( x + vt ) + $ % ( ) * = A sin( kx + + t + ) Wave moving to the left (- x direction) y ( x , t ) = A sin 2 ( x $ vt ) + % ( ) * + = A sin( kx $ , t + ) Wave moving to the right (+ x direction) Common Equations for Waves v = T = k = f k = 2 = 2 T = 2 f v = F T μ = F T l m Superposition of Waves y = y 1 + y 2 = A sin( kx " t ) + A sin( kx " t + ) = 2 A cos 2 % ( ) * sin kx " t + 2 % ( ) * Standing Waves : A special case of superposition of waves where the two waves have the same amplitude, frequency, wavelength, and phase angle but travel in the opposite direction. y = y 1 + y 2 = A sin( kx " t ) + A sin( kx + t ) = 2 A cos t ( ) sin kx ( ) Standing Waves (Same Boundaries) Standing Waves (Mixed Boundaries) f n = v = n 2 L v = n 2 L F T n = 1,2,3… f n = v sound = n 4 L v sound n = 1,3,5… n : number of loops n : number of loops L : length of string L : length of string/air column f n : n th harmonic/mode v sound : 343 m/s f 0 : fundamental frequency Same boundaries mean its ends are either both open or both closed. This mainly applies to waves
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: on strings with both ends tied. However, this also applies to air columns where both ends are open, though the first case is more common. Mixed boundaries are usually an air column with one opening. Keep in mind that n can only take on odd values. Doppler Effect f ' = f v sound + v obs v sound " v source v obs : velocity of observer; positive when moving toward source, negative if moving away v source : velocity of source; positive when moving toward observer, negative if moving observer v sound : 343 m/s f : original sound frequency f : Doppler shifted frequency...
View Full Document

This note was uploaded on 10/26/2011 for the course PHYSICS 1B taught by Professor Corbin during the Spring '11 term at UCLA.

Ask a homework question - tutors are online