10 Superposition

Kindly refer to the online lecture schedule for this topic here

T3W7:

Lesson 1:   Notes pg 1 to 7 (Diffraction, Superposition, Coherence, Interference), 36 minutes.

T3W7:

Lesson 2:   Notes pg 7 to 14 (Two-source interference, Young’s Double Slit, Resultant Intensity), 38 minutes + Checkpoint Question 1.

Try the following Checkpoint Questions. Answers are found at the bottom of this sub-page.

T3W8:

Lesson 3:   Notes pg 15 to 19 (Single-slit Diffraction, Resolving Power, Rayleigh’s Criterion), 37 minutes.   

T3W8:

Lesson 4:   Notes pg 19 to 24 (Diffraction Grating, Diffraction of White Light, Overlapping of Orders), 37 minutes.       

T3W9:

Lesson 5:   Notes pg 24 to 35 (Stationary Waves, Formation, Characteristics, Experiments, Stationary Sound Waves), 51 minutes.                           

T3W9:

Lesson 6:   Video solutions to the following Tutorial Questions:

Q1, Q5, Q6, Q7, Q8, Q9, Q10, Q12, Q13, Q14, Q17, Q19, Q24, Q26, Q28

Stationary waves Q & A 

1. What does "in phase" mean?

When two particles are "in phase", they move in the same direction all the time e.g. move up and move down together at all times. They may move at different speed or distance but that does not matter as long as they are in the same state of vibration (imagine moving in the same direction) all the time. All particles within the same loop in a statioanry waves are in the same state of vibration. Particles in adjacent loops are antiphase (they always move in opposite direction).

2. How can you tell the mode of vibration e.g. whether it is 2nd or 3rd harmonics?

You draw the stationary wave for the fundamental mode with reference to the boundary conditions (fixed/free ends for rope/string, open/closed ends for air column). Other modes of vibration are defined with respect to the fundamental mode. When you draw any other mode of vibration, if the frequency is 3x the freq of the fundamental mode, it is call the 3rd harmonics. If it is 2x, it is call the 2nd harmonics. The relationship for wavelength is then opposite (as v = f λ , when f increases, wavelength decreases as v = constant for the same medium) , if wavelength is halved, it is 2nd harmonics. If wavelength is reduced 5 times, it is the 5th harmonics. So the key is to  - draw the fundamental mode - draw other modes and compare with the fundamental

3. What are pressure nodes?

"Nodes" are so named as the amplitude is always 0. You will notice from the animation in the video, position of displacement antinode is the position where the pressure hardly changes. Unlike the position of displacement antinode where the surrounding particles will move towards it creating a region of high pressure (compression) at one moment and move away from it creating a region of low pressure (rarefaction). Displacement node (with reference to the vibration of the particles from its equilibrium position) are thus "Pressure antinode" cos that is the region where pressure change is the greatest. 

4. What are boundary conditions for standing waves in string/rope and air column?

Boundary conditions are the rule you apply to the ends of a rope/string or air column based on if the ends are fixed/free (for rope/string) or closed/open(for air column). For example, if both ends of a string are fixed to something that prevent it from moving e.g G-clamp in the video applet, these two ends must be nodes. Then you draw the simplest stationary waveform that has both ends with nodes (must be N   A    N) as fundamental frequency. If you have a straw, both ends of a straw are open and the air molecules are free to move at these ends, these two ends must antinode with maximum amplitude. Then you draw the simplest stationary waveform that has both ends with antinodes (must be A   N    A) as fundamental frequency. Go back to the drawings in the video and see if you can identify these rules at the ends boundary conditions that tell you if the ends are N or A.