Two sounds, one of 200 Hz and one of 194 Hz occur at the same time. What beat frequency do you hear? Show your calculations

Question

I'm not looking for someone to do my homework for me. I just don't know what formula to use to figure it out.

Answer 1

http://en.wikipedia.org/wiki/Beat_%28acoustics%29

basically you have

197 Hz + 3 Hz
and
197 Hz - 3 hz
use
sin (p) + sin (q) = 2 sin(1/2)(p+q) cos(1/2)(p-q)

Answer 2

assume 2 pi t everywhere in those trig functions
here p = 200 and q = 194
(1/2) (p+q) = our mean of 197
(1/2)(p-q) = 3
so
sin p + sin q = 2 sin 197* 2 pit sin 3* 2 pi t
so the beat signal is
sin 3 * 2 pi t

f = 3 Hz

Answer 3

sin p + sin q = 2 sin 197* 2 pit cos 3* 2 pi t
so the beat signal is
cos 3 * 2 pi t
6
The envelope frequency is therefore 3 Hz but we will hear a maximum of the 197 HZ signal twice per period of the envelope, thus we will hear the original difference frequency of 6 Hz