| Engineering Acoustics - EEN502 Michael Battaglia Project 1 |
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Part 1 - ObjectiveLet a sound source produce a single tone at frequency F0. The source is moving on a straight line that passes “through” the observer. Plot the velocity of the source relative to the observer, the signal envelope, and the apparent frequency of the source as functions of time. Generate the sound at the position of the observer. Solution: Matlab Code To implement this, I simply treated the trajectory of the source as a horizontal line on which the observer is placed. The source is initially placed at the far left of the line, and moves towards the far right. Here is a screenshot of the plots for when the length of the trajectory is 100 m, the velocity is 50 m/s, and the observer is located at 50 m from the left of the start trajectory. For reference, the tone being emitted by the source in this picture is 440 Hz. Note that the velocity and frequency plots are clipped: the spots on the plot where no value appears signifies that the values are at the maximum value allowed and are simply being covered up by the axes. The pressure envelope was calculated by simply taking the reciprocal of the distance between the source and the observer. Since the envelope will be a function of air pressure, not power, the relationship between the pressure envelope and the distance will be inverse proportional. Since in this example, the source "passes through" the observer, there is a point where source and observer meet at which the pressure envelope value is 1/0, or theoretically infinite. To represent this in the audio clip, we simply constrained the signal output to (-1, 1) by clipping the signal. This means that as the signal "passes through" the observer, odd harmonic distortion will be produced as the signal clips. Note also that the radial velocity is counted as negative when the source particle is headed towards the observer: this is because the radius is indeed getting smaller at this phase. For comparison, here is another plot. The trajectory here is 20 m, the velocity 10 m/s, and the observer is located on the right at 15 m from the source origin. The source is emitting a 1000 Hz tone. |
