Jim Kelley wrote:

> David L. Wilson wrote:
>
>> "Jim Kelley" <jwkelley@uci.edu> wrote in message
>> news:f6ujcc$jd0$1@news.service.uci.edu...
>> ...
>>
>>>sin(a) + sin(b) = 2sin(.5(a+b))cos(.5(a-b))
>>>
>>>A plot of the function reveals that cos(.5(a-b)) describes the envelope.
>>
>>
>> Ok.
>>
>> The period of the 'enveloped' waveform (or the arcane, beat
>>
>>>modulated waveform) then can be seen to vary continuously and
>>>repetitiously over time - from 1/a at one limit to 1/b at the other.
>>
>>
>> ?
>>
>>
>>>At a particular instant in time the period does in fact equal the average
>>>of the two. But this is true only for an instant every 1/(a-b) seconds.
>>
>>
>> ??
>>
>> How do you come up with anything but a period of of the average of the
>> two for the enveloped waveform?
>
> The error here is in assuming that the sin and cos terms in the
> equivalent expression are representative of individual waves. They
> are not. The resultant wave can only be accurately described as the
> sum of the constituent waves sin(a) and sin(b), or as the function
> 2sin(.5(a+b))cos(.5(a-b)). That function, plotted against time
> appears exactly as I have described. I have simply reported what is
> readily observable.
>
> jk


I would submit you plotted it wrong and/or misinterpreted the results.