# Calculate 25 ms of a 260 Hz cosine wave with amplitude 1, and sample rate 0.1 ms (milliseconds)…

I . Calculate 25 ms of a 260 Hz cosine wave with amplitude 1, and sample rate 0.1 ms (milliseconds) and plot the result. 2. Calculate 25 ms of a 347 Hz cosine wave with amplitude 0.5 and 25 ms of a 390 Hz cosine wave. Use the same sample rate as in 1) and add it to the sinusoid in 1). Plot the result. 3. Apply a minimum shift (scalar addition) to the sinusoids in 1) and 2) such that the sinusoids have no negative values. Document clearly how you are doing this in your code. Plot the sinusoids on the same graph. 4. Phase shift the 260 Hz wave by -45° and the 390 Hz wave by 45°, sum these waves together with the 347 Hz wave, and plot the resulting cosine. Discuss the differences in this plot compared with 2) above. What is occurring? 5. Calculate 25 ms of an exponential with damping constant=-25. Damp the sinusoids in 3) with the exponential and plot the results on the same graph. What would the chord sound like after damping? 6. Shift the exponential function calculated in 5) such that it is delayed by 10 ms. Plot the result. 7. Approximate the dime delta (5 = 1 where t3; 0 otherwise) function within the interval -1 to 1 by a summation of 25 cosine functions with integer frequencies f=1, 2, 3 … 25 Hz. Use the sample interval of 0.01 s. Increase the number of cosines to 50 and 100. Turn in plots that including the total number of cosines and the resulting stacked function that represents the approximation of the dirac delta function. Comment about the form that the stacked function takes as you increase the number of harmonics. What can you conclude about the composition of the dime delta function. Why do you think this function is sometimes used to simulate seismic sources (e.g., an explosion)?

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