Vid 5: sum(hms) incorrect?

[AidanGG]

In the cell labelled In [126], you have

all_harmonics=True
if all_harmonics:
    tot = sol.sum(axis=1)[::10] # all harmonics
else:
    tot = sum(hms)[::10] # only first 10 harmonics
tot = tot.astype(np.float32)

When calculating with all_harmonics, you take the average y value across the string at each time t to generate your PCM sound stream (this makes sense). The average value of a periodic function is just the amplitude of its zeroth harmonic; summing all harmonic amplitudes at a timeslice t is a different calculation. You can check this by listening to WAVs with all_harmonics=True vs all_harmonics=False with a high number of harmonics and finding that they don't sound similar.

Edit: Actually I'm not sure if taking the average y value at each time t is correct, since even harmonic contributions to the average y would be zero. Here's an open SE question on the topic: https://physics.stackexchange.com/questions/574906/derive-shape-of-sound-wave-from-vibrating-string-simulation