30. If you mix two pure tones with frequencies of 100 Hz and 102 Hz

Moderator: bjkwon

Post Reply
bjkwon
Posts: 111
Joined: September 26th, 2018, 9:36 pm

30. If you mix two pure tones with frequencies of 100 Hz and 102 Hz

Post by bjkwon » June 14th, 2020, 6:07 pm

You will have a tone of 101 Hz, the average of the two frequencies, with its amplitude oscillating at the rate of 2 Hz, the frequency difference. This makes perfect sense: following the Product-Sum Identity of sine and cosine{ref}, the right hand side of the equation is the product of the two terms, one for the average frequency and the other for the difference frequency. Known as "beats," this is a textbook definition of AM[amplitude modulation]. We indeed hear a 101-Hz tone pulsating 2 times a second. Beautiful, isn't it? The equation captures everything we perceive.

Image

Post Reply