Physics 5B Lecture 10 February 3 2012 Chapter 15 Wave Reflection Chapter 16 Sound Midterm Exam Scores 30 25 Studen nts 20 15 10 5 0 0 20 40 60 80 100 120 Score Mean 69 Median Mean 69 Median 73 73 Std Std Dev Dev 19 19 Min 25 Max 99 Number of exams 153 Breakpoints from syllabus 83 A 63 B 45 C Wave Interference in 2D http phet colorado edu en simulation wave interference Reflection Wave on a String g http phet colorado edu en simulation wave on a string Law of Reflection 2D or 3D Note that the rays are perpendicular to the wave fronts although they may not look like it to the eye optical illusion This law ensures that the two purple dashed paths for example l are equall in distance Fig 15 21 Angle of reflection Angle of incidence Reflection at a Boundary fast slow Common examples light waves incident upon a window Sound waves hitting a wall Bell Wave Machine We now know how to tell if the reflected pulse will be inverted or not but can we calculate the amplitudes of the reflected and transmitted waves Thatt iis nott hard Th h d to t do d ffor th the case off hharmonic i periodic i di waves See Problem 15 40 in the textbook 15 40 Problem 15 fast slow v1 v2 v1 x 0 v2 Wave incident from the left x 0 D A sin k1x t DR AR sin k1x t k1 k2 x 0 DT AT sin k 2 x t Require continuity D 0 t DR 0 t DT 0 t R i smooth Require th D D D R T x x 0 x x 0 x x 0 k k v v AR 1 2 A 2 1 A k1 k 2 v2 v1 Assume that the rope is not broken andd ddoesn t t hhave a kink in it I changed the notation from what is in the book for better clarity 15 40 MathCad Animation of 15 fast slow l http scipp ucsc edu http scipp ucsc edu johnson phys5b johnson phys5b Reflection xvid avi BLUE is the incident wave The wave velocity for x 0 is twice the wave velocity for x 0 MAGENTA is i the h reflected fl d wave RED is the sum total wave actual shape of the rope Standing Waves Interference of two waves off equall frequency f and d amplitude but moving in opposite directions on the string string See the MathCad animation y x t 2 A sin i kx k cos t http scipp ucsc edu johnson p pp j phys5b StandingWave xvid avi Standingg wave on a stringg L 2 f1 fundamental frequency lowest possible If the waves reflect from both ends of the string then the interference will be destructive unless a standing wave can form with a node at each end of the string If the length density and tension of the string are chosen and fixed then only the frequency is left to vary The string will resonate when the frequency is a harmonic of the fundamental frequency Standingg Wave Harmonics L n f v 1 2 FT Standing Wave Demo Standingg Wave Question A string is clamped at both ends and then plucked so that it vibrates in a standing mode between two extreme positions a and cc Let upward motion correspond to positive velocities velocities When the string is in position b the instantaneous velocity of points along the string is a b c A B C D Up is positive and zero everywhere h down is negative negative everywhere positive everywhere in different directions at different locations 15 49 Problem 15 If two successive harmonics of a vibrating string are 240 Hz H and d 320 H Hz what h is the h frequency of the fundamental A 40 Hz B 80 Hz B H C 120 Hz D 240 Hz Plucked String When you pluck a string you hold it in a triangle shape not the shape of a sine wave Remember Fourier a triangle is composed of a series of sine or cosine waves added together When the string is released all of those harmonics will begin vibrating simultaneously Vibratingg Triangle g Wave See the MathCad animation of this wave http scipp ucsc edu johnson phys5b SawTooth xvid avi phys5b SawTooth xvid avi Bowed Violin String Hermann von Helmholtz Helmholtz about 140 years ago ago Taken from http plus maths org content why violin so hard play Sound and Sound Waves CHAPTER 16 Sound Pressure Waves Zero displacement A point i t off maximum displacement