The discussion revolves around understanding beat frequencies in sound waves, particularly the relationship between the frequencies of two sound waves and the resultant tone produced. Participants are exploring the concepts of frequency fluctuation and average frequency in the context of sound wave interference.
The discussion is active, with participants engaging in mathematical reasoning about the summation of sound waves and how it relates to beat frequencies. Some guidance has been offered regarding the mathematical representation of sound wave interference, but there is no explicit consensus on the interpretations being explored.
Participants are considering the implications of similar values for the frequencies involved and how this affects the perceived sound and its representation mathematically. There is an ongoing examination of assumptions related to frequency averages and their auditory effects.
Yes.Sho Kano said:
Consider summing two tones of the same amplitude, A sin(ωt)+A sin(ψt). Do you know a way to write that as a product of trig functions?Sho Kano said:
##2A[sin(\frac{wt+ \varphi t}{2})cos(\frac{wt-\varphi t}{2})]## There's an average in the sine, but not in the cosine, how does this relate to an average freq?haruspex said:
Assuming ψ and ω are similar in value, that product has one frequency as the average of those and the other factor a much lower frequency. Mathematically that does not make them fundamentally different, but to a human observer it will sound and look like a wave of the average frequency with an amplitude varying at the much lower (beat) frequency.Sho Kano said: