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Lecture Physics A2: Interference - PhD. Pham Tan Thi

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Lecture Physics A2: Interference - PhD. Pham Tan Thi present the content a single oscillating wave, multiple waves - superposition, superposing sinusoidal waves, adding sine waves with different phases,...

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Nội dung Text: Lecture Physics A2: Interference - PhD. Pham Tan Thi

  1. Interference Pham Tan Thi, Ph.D. Department of Biomedical Engineering Faculty of Applied Science Ho Chi Minh University of Technology
  2. A Single Oscillating Wave The formula y(x, t) = Acos(kx !t) describes a harmonic plane wave of amplitude A moving in the +x direction For a wave on a string, each point on the wave oscillates in the x direction with simple harmonic motion of angular frequency ω 2⇡ ! The wavelength = The speed/velocity v = f = k k The intensity is proportional to the square of the amplitude I / A2
  3. Multiple Waves: Superposition The principle of superposition states that when two or more waves of the same type cross at a point, the resultant displacement at that point is equal to the sum of the displacements due to each individual wave. For inequal intensities, the maximum and minimum intensities are: Imax = |A1 + A2|2 Imin = |A1 - A2|2
  4. Multiple Waves: Superposition Constructive “Superposition” Destructive “Superposition”
  5. ou added the two sinusoidal waves shown, Superposing Sinusoidal Waves at would the result look like? If we added the two sinusoidal waves shown, what would the result look like? 1 .0 0 0 .5 0 0 .0 0 1000 100 200 300 400 500 600 700 800 900 0 - 0 .5 0 - 1 .0 0 of two sines having the same frequency is another same frequency. ude depends on their relative phases. 2 .0 0 1 .5 0 1 .0 0 0 .5 0
  6. ou added the two sinusoidal waves shown, 1 .0 0 0 .5 0 Superposing Sinusoidal Waves at would the result look like? 0 .0 0 1000 100 200 300 400 500 600 700 800 900 0 - 0 .5 0 If we added the two sinusoidal waves shown, what would the result - 1 .0 0 look like? 1 .0 0 0 .5 0 0 .0 0 of two sines having the same frequency is another s 1000 100 200 300 400 500 600 700 800 900 0 - 0 .5 0 - 1 .0 0 same frequency. The sum of two sines having the same frequency is another sine ude depends with the sameon their→ relative frequency Its amplitudephases. depends on their relative phases of two sines having the same frequency is another 2 .0 0 1 .5 0 same frequency. 1 .0 0 0 .5 0 ude depends on their relative phases. 0 .0 0 0 100 200 300 400 500 600 700 800 900 1000 - 0 .5 0 - 1 .0 0 - 1 .5 0 2 .0 0 - 2 .0 0 1 .5 0 1 .0 0 0 .5 0
  7. Adding Sine Waves with Different Phases Suppose we have two sinusoidal waves with the same A1, ω and k: y1 = A1 cos(kx !t) and y2 = A1 cos(kx !t + ) One starts at phase 𝜙 after the other Spatial dependence of 2 waves at t = 0 Resulting wave: y = y1 + y 2 ✓ ◆✓ ◆ ↵ +↵ A1 (cos↵ + cos ) = 2A1 cos 2 2 y1 + y 2 y = 2A1 cos(( /2) /2)cos(kx !t + /2) y = 2A1 cos( /2)cos(kx !t + /2) Amplitude Oscillation
  8. What happens when two waves are present at the same place? Interference of Waves Always add amplitudes (pressures or electric fields). WhatHowever, happens when two waves we observe are present intensity at the same place? (power). ForAlways equal Aadd andamplitude ω: (e.g. pressures or electric fields) However, we observe intensity (i.e. power) For equal A = ω: A and 2A1 cos(φ / 2) ⇒ I = 4I1 cos (φ / 2) 2 A = 2A1cos(𝜙/2) I = 4I1cos2(𝜙/2) Example: Terminology: Stereospeakers: Stereo speakers: Listener: Constructive interference: Terminology: waves are “in phase” Constructive (φ = 0, interference: 2π, 4π, ..) Listener: waves are “ininterference: phase” Destructive waves (𝜙 = 0, are “out of phase” 2π, 4π,…) (φ = π,interference: Destructive 3π, 5π, …) waves are “out of phase” (𝜙 = π, 3π, 5π,…) Of course, φ can take on an infinite number of values. We won’t use terms like “mostly constructive” or “slightly destructive”. Lec
  9. Quiz Each speaker alone produces an intensity of I1 = 1 W/m2 at the Example: Changing phase of the Source listener: Example: Changing phase of the Source Each speaker alone produces an intensity of I = 1 W/m2 at the listener: 1 Each speaker alone produces an intensity of I1 = 1 W/m2 at the listener: Example: Changing phase I = I = of A =the 1 W/mSource I = I1 = A12 = 1 W/m2 1 1 2 2 I =1 IW/m Each speaker alone produces an intensity of I1 = 1 = A1 at=the 22 1 W/m 2 listener: Drive the speakers in phase. What is the intensity I at the listener? DriveDrive thethespeakers in What speakers in phase. phase. IWhat 2 is = I1 = AI1at is the intensity 1the =the W/m 2 intensity I at the listener? listener? I= Drive the speakers in phase. What is the intensity I =I at the listener? I =? Now shift phase of one speaker by 90o.What is the intensity I at the listener? I= Now shift phase of one speaker by 90o.What is the intensity I at the listener? Now shift phase of one speaker by 90°. What is the intensity I at the listener? I= Now shift phase of one speaker by 90o.What is the intensity I at the listener? I= φ φ Lecture 2, p.7 I =? Lecture 2, p.7 I= φ Lecture 2, p.7
  10. Quiz Each speaker alone produces an intensity of I1 = 1 W/m2 at the Example: Changing phase of the Source listener: Example: Changing phase of the Source Each speaker alone produces an intensity of I = 1 W/m2 at the listener: 1 Each speaker alone produces an intensity of I1 = 1 W/m2 at the listener: Example: Changing phase I = I = of A I=the = I1Source 1 W/m = A12 = 1 W/m2 1 1 2 2 I =1 IW/m Each speaker alone produces an intensity of I1 = 1 = A1 at=the 22 1 W/m 2 listener: Drive the speakers in phase. What is the intensity I at the listener? DriveDrive thethespeakers in What speakers in phase. phase. IWhat 2 is = I1 = AI1at is the intensity 1the =the W/m 2 intensity I at the listener? listener? I= Drive the speakers in phase. What is the intensity I = (2A1)2 = 4I1 = 4 W/m2 I =I at the listener? Now shift phase of one speaker by 90o.What is the intensity I at the listener? I= Now shift phase of one speaker by 90o.What is the intensity I at the listener? Now shift phase of one speaker by 90°. What is the intensity I at the listener? I= Now shift phase of one speaker by 90o.What is the intensity I at the listener? I= φ φ Lecture 2, p.7 I =? Lecture 2, p.7 I= φ Lecture 2, p.7
  11. Quiz Each speaker alone produces an intensity of I1 = 1 W/m2 at the Example: Changing phase of the Source listener: Example: Changing phase of the Source Each speaker alone produces an intensity of I = 1 W/m2 at the listener: 1 Each speaker alone produces an intensity of I1 = 1 W/m2 at the listener: Example: Changing phase I = I = of A I=the = I1Source 1 W/m = A12 = 1 W/m2 1 1 2 2 I =1 IW/m Each speaker alone produces an intensity of I1 = 1 = A1 at=the 22 1 W/m 2 listener: Drive the speakers in phase. What is the intensity I at the listener? DriveDrive thethespeakers in What speakers in phase. phase. IWhat 2 is = I1 = AI1at is the intensity 1the =the W/m 2 intensity I at the listener? listener? I= Drive the speakers in phase. What is the intensity I = (2A1)2 = 4I1 = 4 W/m2 I =I at the listener? Now shift phase of one speaker by 90o.What is the intensity I at the listener? I= Now shift phase of one speaker by 90o.What is the intensity I at the listener? Now shift phase of one speaker by 90°. What is the intensity I at the listener? I= Now shift phase of one speaker by 90o.What is the intensity I at the listener? I= φ φ Lecture 2, p.7 I = 4I1cos2(45°) = 2 I1 = 2 W/m2 Lecture 2, p.7 I= φ Lecture 2, p.7
  12. ACT 1: Noise-cancelling Noise Cancelling Headphones Headphones Noise-canceling Noise-canceling headphones headphones workingwork using using interference. interference. A microphone A microphone on theon the earpiece earpiece monitors monitors the instantaneous the instantaneous amplitude of the amplitude external of the and sound wave, external soundon a speaker wave, the inside and a speaker on the inside of the of the earpiece produces a sound wave cancel it. earpiece produces a sound wave to cancel it. 1. must 1. What Whatbe must the be the phase phase of the signal of the signal from thefrom the speaker speaker relativerelative to the to the externalexternal noise? noise? a. 0a. 0 b. 90˚ c. πc. π b. 90 d. d. 180-180˚ e.e.2π2π 2. What must the intensity Is of the signal from the speaker relative to the external noise? 2. What must be the intensity Is of the signal from the speaker relative to the a. Iexternal s = In b. Is < IInn? c. Is > In noise a. Is = In b. Is < In c. Is > In Lecture 2, p.10
  13. ACT 1: Noise-cancelling Noise Cancelling Headphones Headphones Noise-canceling Noise-canceling headphones headphones workingwork using using interference. interference. A microphone A microphone on theon the earpiece earpiece monitors monitors the instantaneous the instantaneous amplitude of the amplitude external of the and sound wave, external soundon a speaker wave, the inside and a speaker on the inside of the of the earpiece produces a sound wave cancel it. earpiece produces a sound wave to cancel it. 1. must 1. What Whatbe must the be the phase phase of the signal of the signal from thefrom the speaker speaker relativerelative to the to the externalexternal noise? noise? a. 0a. 0 b. 90˚ c. πc. π b. 90° d. d. 180° -180˚ e.e.2π2π Destructive interference occurs when the waves are ±180° out of phase (=π radians) 2. What must the intensity Is of the signal from the speaker relative to the external noise? 2. What must be the intensity Is of the signal from the speaker relative to the a. Iexternal s = In b. Is < IInn? c. Is > In noise a. Is = We In want b. IAs =< AIns - Anc. = I0. > s Note In that I is never negative. Lecture 2, p.10
  14. Interference of Light
  15. Review: Lights of Different Colors Long wavelength (Low frequency) Short wavelength (High frequency) Violet light has the highest energy in visible region
  16. Interference of Light Interference is a phenomenon in which two coherent light waves superpose to form a resultant wave of greater or lower amplitude (a) Constructive interference: If a crest of one wave meets a crest of another wave, the resultant intensity increases. (a) Destructive interference: If a crest of one wave meets a trough of another wave, the resultant intensity decreases.
  17. Light Polarization
  18. Conditions for Interference ✓ Two interfering waves should be coherent, i.e. the phase difference between them must remain constant with time. ✓ Two waves should have same frequency. ✓ If interfering waves are polarized, they must be in same state of polarization. ✓ The separation between the light sources should be as small as possible. ✓ The distance of the screen from the sources should be quite large. ✓ The amplitude of the interfering waves should be equal or at least very nearly equal. ✓ The two sources should be narrow. ✓ The two sources should give monochromatic or very nearly monochromatic.
  19. Young’s Double Split Experiment • In 1801, Young admitted the sunlight through a single pinhole and then directed the emerging light onto two pinholes. • The spherical waves emerging from the pinholes interfered with each other and a few colored fringes were observed on the screen.
  20. Calculation of Optical Path Difference between Two Waves As slits (S1 and S2) are equidistant from source (S), the phase of the wave at S1 will be same as the phase of the wave at S2 and therefore S1, S2 act as coherent sources. The waves leaving from S1 and S interfere and produce alternative bright and dark bands on the screen. 2d is the distance between S1 and S2 θ is the angle between MO and MP x is the distance between O and P Let P is an arbitrary point on screen, which is at a distance D from source S1N is the normal on to the line S2P S1M = S2M = GO = OH = d
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