Math Is Fun Forum

hill0093

Member

Registered: 2013-07-24

Posts: 2

trignometry

From common trigonometric formulas, I know that 
A cos(2πF1t) + A cos(2πF2t) = 2A cos(2π[(F1-F2)/2]t) cos(2π[(F1+F2)/2]t) 
where A is the amplitude of both original cosine functions of t,  and F1 and F2 are their respective frequencies, the product demonstrates a modulation of the cosine of the average frequency.
Is there a similar product formula if the two original amplitudes are different, i.e..:
A1 cos(2πF1t) + A2 cos(2πF2t) = ?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: trignometry

hi hill0093

Welcome to the forum.

I hung on hoping someone who knows the answer would post, but it doesn't look like they will    so I'll jump in with what little I know .  Maybe that will spur someone else to tell me I'm wrong and then we'll get somewhere. 

The first result comes from this trig formula

http://www.sosmath.com/trig/prodform/prodform.html

So it works because the amplitudes are the same.

I'm fairly certain there's no formula when the amplitudes are different.  There might be one when one amplitude is a simple factor of the other.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

hill0093

Member

Registered: 2013-07-24

Posts: 2

Re: trignometry

Thanks Bob.
That's what I suspected.
I'll just plot graphically what I want to see.