Physics 5B Lecture 9 February 1 2012 Chapter 15 Waves Example Periodic Wave T is the period of the upand down oscillation of an individual point on the string v T v f Harmonic Periodic Wave v f v EEvery point i on the h string i is i making ki a harmonic h i oscillation up and down http phet colorado edu en simulation wave on a string Harmonic Periodic Waves D x t A sin k x t Harmonic Oscillation of the point on the string at x 0 T 2 2 and k T Shape of the string at time 0 Some animations of harmonic waves v f http scipp ucsc edu johnson applets Wave SHM htm http scipp ucsc edu johnson applets wavelength period htm k The graph below shows a snapshot of a wave on a string th t iis ttraveling li to t th i ht Th i a bit off paint i t on th that the right There is the string at point P y vwave P Q x At the instant shown the velocity of paint point P has hi h di ti which direction A B C D D Up Down Left Ri ht Right The graph below shows a snapshot of a wave on a string that is traveling to the right There is a bit of paint on the string at point P y vwave P Q x At the instant shown the acceleration of paint point P has hi h di ti which direction A B C D D Up Down Left Ri ht Right Problem 15 15 25 D x t A sin k x t A 0 026 m k 45 m 1 1570 rad s 0 66 rad Consider the point x 1 00 m on the cord of Example 15 5 Determine a The maximum velocity of the point point and b The maximum acceleration c What are the velocityy and acceleration at t 2 50 s d What is the phase velocity of the wave Power Transported by a Wave The most important p point p to remember is that the power energy per unit time transported p byy a wave is proportional p p to the square of the amplitude and the square q y of the frequency 2 2 I 1 v A 2 15 7 For a wave moving through a volume e g e g sound intensity is power per unit area We will come back to this in the next chapter chapter Superposition A tremendously important subject in physics Waves Optics Electricity and Magnetism Quantum Mechanics etc Property of linear differential equations e g the wave equation http phet colorado edu en simulation fourier MathCad Fourier Examples The red curve i a simple is i l sum of the cosine waves shown above MathCad Fourier Examples The red curve is a simple sum of the sine waves shown above b MathCad Fourier Examples The red curve is a simple sum of the sine waves shown above b A string has two pulses approaching each other moving 1 m s 1m What will the string look like 3 sec later A B C D 1m 1m 1m 1m E 1m