Purdue University, Physics 220 Mean: 65.7 (or 55%) Std. Dev.: 21.1 Lecture 20 Purdue University, Physics 220

Purdue University, Physics 220 Lecture 20 Waves Lecture 20 Purdue University, Physics 220

Constructive Interference The net disturbance is the sum of the individual disturbances. When waves cross in a point and have the same sign amplitude, they add constructively. Since intensity is proportional to amplitude squared, the resulted intensity is more than the sum of the intensities of individual waves. Lecture 20 Purdue University, Physics 220

Destructive Interference The net disturbance is the sum of the individual disturbances. When waves cross in a point and have the opposite sign amplitude, they add destructively. Since intensity is proportional to amplitude squared, the resulted intensity is less than the sum of the intensities of individual waves. Lecture 20 Purdue University, Physics 220

Purdue University, Physics 220 Interference Out of phase by = Out of phase by =(2/3) In phase =0 Fully Destructive Destructive Constructive Destructive Lecture 20 Purdue University, Physics 220

Coherence and Interference Two waves are coherent when their frequencies are same and they maintain a constant phase difference. A path difference L of  corresponds to a phase difference  of 2 Lecture 20 Purdue University, Physics 220

Purdue University, Physics 220 Interference Coherent waves may interfere constructively or distructively. For constructive interference: Amplitudes add: A=A1+A2 For destructive interference: Amplitudes subtract: A=|A1-A2| Lecture 20 Purdue University, Physics 220

Purdue University, Physics 220 Interference Lecture 20 Purdue University, Physics 220

Purdue University, Physics 220 Interference The total amplitude (thus intensity) at each location depends on phase shift between two waves. Constructive: Destructive: Maxima with twice the amplitude occur when phase shift between two waves is 0, 2, 4, 6 … (or path difference is 0, , 2…) Minima with zero amplitude occur when phase shift between two waves is , 3, 5 … (or path difference is 0, /2, 3/2…) Lecture 20 Purdue University, Physics 220

Purdue University, Physics 220 Intensity Constructive interference: I > I1 + I2 Destructive interference: I < I1 + I2 Incoherent superposition: I = I1 + I2 Lecture 20 Purdue University, Physics 220

Purdue University, Physics 220 Diffraction Diffraction is the spreading of a wave around an obstacle in its path. Lecture 20 Purdue University, Physics 220

Purdue University, Physics 220 Reflection When a wave strikes an obstacle or comes at the end of the medium it is travelling in, it is reflected (at least in part). If the end of the rope is fixed the reflected pulse is inverted If the end of the rope is free the reflected pulse is not inverted Lecture 20 Purdue University, Physics 220

Purdue University, Physics 220 Reflection When a wave travels from one boundary to another, reflection occurs. Some of the wave travels backwards from the boundary Traveling from fast to slow inverted Traveling slow to fast upright Lecture 20 Purdue University, Physics 220

Purdue University, Physics 220 Reflection When the end of the rope is fixed to a support the pulse reaching the fixed end exerts a force (upward) on the support. The support exerts a force equal and opposite (downward) on the rope. This downward force generates the inversion that can be thought as a change of phase of 180. If the end of the rope is free it can overshoot. The overshoot exerts an upward pull on the rope and the reflected pulse is not inverted. Lecture 20 Purdue University, Physics 220

Speed of Waves Depends on Medium When a wave reaches a boundary between two different media the speed and the wavelength change, but the frequency remains the same. Lecture 20 Purdue University, Physics 220

Purdue University, Physics 220 Law of Refraction 1 2 Lecture 20 Purdue University, Physics 220

Purdue University, Physics 220 Standing Waves Shake the end of a string If the other end is fixed, a wave travels down and it is reflected back  interference The two waves interfere => standing wave Nodes when sin (kx)=0: Anti-nodes sin (kx)=+/- 1, half way between nodes Anti-nodes nodes Lecture 20 Purdue University, Physics 220

Purdue University, Physics 220 iClicker A standing wave on a string is given by: Is there a node or antinode at x=0? A) Node B) antinode C) neither node nor antinode Lecture 20 Purdue University, Physics 220

Purdue University, Physics 220 iClicker What is the distance between nodes? A wavelength/4 B wavelength/3 C wavelength/2 D wavelength/1 Lecture 20 Purdue University, Physics 220

Purdue University, Physics 220 Standing Waves The natural frequencies are related to the length of the string L. The lowest frequency (first harmonic) has one antinode The second harmonic has two antinodes The n-th harmonic Lecture 20 Purdue University, Physics 220

Purdue University, Physics 220 Standing Waves Fixed endpoints f = v/l Fundamental n=1 ln = 2L/n fn = n v / (2L) fn = n f1 No energy is transmitted by a standing wave Lecture 20 Purdue University, Physics 220