1 Physics 7C SS1 Lecture 4: Interference 2D interference Time-dependent interference Standing waves

2 Agenda Quickly Refer fundamentals of interference Answer any 1D questions Quiz 1 Review 2D interference (why “d sin  ) Introduce time-dependent interference (beats) Introduce standing waves Begin Ray Model? (if time permits)

3 Interference Fundamentals  = -4 , -2 , 0, +2  … is constructive  = -3 , - , +  … is destructive  =anything else…is partial 2π  2π  Unit circle Wave 1 Wave 2 Difference

4 Quiz 2

5 d Two slits create two overlapping wave fronts Crest Trough 2D Interference

6 Laser Interference A phase chart (and some critical thinking) can illustrate that typically 2-slit interference depends only on path length difference,  x!

7 a b d c e What is  x?

8 Summary: 2D Interference Why calculate d sin  ? Physically measuring  x is impossible for small slits. d sin  estimates the pathlength difference (  x). That is, how much further does the wave travel from slit 1 compared to from slit 2. When the wave splits through the slits, frequency and  don’t (typically) change, so only pathlength matters! Constructive interference occurs if one wave travels a whole number of wavelengths further than the other if  x=n  =0 or 2 , 4 , 6 , etc. Destructive interference occurs if one wave travels a half number of wavelengths further than the other if  x=(n/2)  (for n odd)  =  or 3 , 5 , 7 , etc. …so d sin  = m determines type: constructive, destructive, or partial

9 Interference for differing frequencies: Beats What type of interference occurs at each point?

10 Interference for differing frequencies: Beats 12345

11 Interference for differing frequencies: Beats The carrier frequency The beat frequency