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Weekly Assignments

  1. Syllabus
  1. Class begins August 30
  1. Homework 01
  2. Homework 02
  3. Homework 03
  4. Homework 04
  5. Homework 05
  6. Homework 06
  7. Homework 07
  8. Homework 08, Part 1
  9. Homework 08, Part 2
Bass

Modeling 120Hz bass response in my living room.

The subwoofer is in the upper right corner.

Red= high sound pressure in phase.
Blue= high sound pressure out of phase.
Yellow= low sound pressure.

The mathematical model is a simple one, derived by looking for low amplitude waves in the compressible Navier-Stokes equations.

Plot shows values predicted by a numerical simulation of my mathematical model. These gradients were later confirmed by testing with a decibelmeter.

Bass

Least Squares Estimation of the Temperature on My Walk to School.

A gauge in my home measures the indoor temperature. A remote gauge outside my window measures temperature and sends it, via radio transmitter, to the indoor gauge.

Problem: The outdoor gauge is inside a thermal boundary layer surrounding my building, so it doesn't get an accurate measurement of the true outdoor temperature.

Bad solution: Look up the real temperature downtown on the internet.

My solution: Collect 36 triplets of data for the Downtown temp, the Home temp and the Outdoor (wrong) temp (D,H,O). According to heat conduction/convection theory, O is a linear function (or nearly a linear function) of D and H. Attempt to fit the data to a function of the form O=xD+yH using a least squares minimization to find the coefficients x and y.

The graph shows the plane which minimizes the squares of the errors. Click it for a larger view. The x-axis shows the temperature measured by the outdoor gauge. The y-axis shows the temperature measured by the indoor gauge. The z-axis is the true outdoor temperature found from the National Weather Service Website. Stars show the 36 data points that I collected. This plot can be used to estimate the real outdoor temperature from the two pieces of data that my gauge collects. Predictions so far are within 1 or 2 degrees fahrenheit of accuracy. Errors are likely due to variability in wind speeds.

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