Tap the tuning fork and have one instrument or one singer produce an A to match that tone. You can also use a piano to make the 440 Hz tone. Mathematically, the wave is represented by the expression: amplitude x sin (440 x 2 x pi x time), where the time is measured in seconds.
Play or sing a note close to 440 Hz. When first trying to identify modulation, you might find it easier to hear if the frequency of the second note is very close to 440 Hz, like 441 or 442 Hz. Mathematically, a 442-Hz wave is amplitude2 x sin(442 x 2 x pi x time).
Put the two instruments close to each other so that their sound waves fill the same space. The sound waves in the air are now the sum of the waves from each source. Mathematically, this is sound = amplitude x sin (440 x 2 x pi x time) + amplitude2 x sin(442 x 2 x pi x time).
Apply the trigonometric identity that sin A + sin B = 2 sin (A + B) x cos (A - B). For the sound waves, the total sound is now (amplitude + amplitude2) x sin ((440 + 442)/2) x 2 x pi x time) x cos ((440 - 442)/2) x 2 x pi x time) = total amplitude x sin (441 x 2 x pi x time) x cos (2 x pi x time).
Listen for the modulation. it’s unlikely you’ll be able to notice the difference between the 440 Hz original note and the new 441 Hz note, but you will notice the 2 Hz frequency. The 2 Hz modulation has the effect of changing the amplitude of the sound wave from zero to maximum and back to zero every second. That’s called a beat frequency, and it’s fairly easy to hear.