The Physics
Hypertextbook
Opus in profectus

# Interference & 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 + 1 sin 3x + 1 sin 5x + 1 sin 7x +… 3 5 7

 y = ∑ 1 sin(2n − 1)x 2n − 1
2.  y = sin x − 1 sin 2x + 1 sin 3x − 1 sin 4x +… 2 3 4

 y = ∑ (− 1)n +1 sin nx n
3.  y = cos x + 1 cos 3x + 1 cos 5x + 1 cos 7x +… 9 25 49

 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 the parts of your body that are moving…
1. in phase with each other
2. out of phase with each other
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.