Interference and Superposition

Problems

practice

1. Write something.
2. Write something else.
3. Graph the following Fourier series with enough detail that you can determine basic shape of each wave.

   1. y = sin x + ¹₃ sin 3x + ¹₅ sin 5x + ¹₇ sin 7x +…

      y = ∑	1	sin(2n − 1)x
      	2n − 1

   2. y = sin x − ¹₂ sin 2x + ¹₃ sin 3x − ¹₄ sin 4x +…

      y = ∑	(− 1)n +1	sin nx
      	n

   3. y = cos x + ¹₉ cos 3x + ¹₂₅ cos 5x + ¹₄₉ cos 7x +…

      y = ∑	1	cos(2n − 1)x
      	(2n − 1)2

4. Write something completely different.

conceptual

1. Walking involves the coordinated periodic motion of various parts of your body. Identify any two body parts that are moving…
   1. in phase with each other
   2. out of phase with each other
   …when a typical person is walking.
2. Graph the superposition of two sine curves with slightly different frequencies.

   1. y =	sin(1.00 x) + sin(1.10 x)
      xmin =	0 radians
      xmax =	100~200 radians

   2. y =	sin(1.00 x) + sin(1.01 x)
      xmin =	0 radians
      xmax =	1000~2000 radians

3. worksheet-superposition.pdf
   These unusually shaped wave pulses are heading towards each other in a medium whose wave speed is one grid unit per second. Draw the resulting shape of the medium one, two, three, and four seconds later.