Hearing Subtraction
- an activity on frequency and beats -

Can you know the answer to a subtraction problem before you know which numbers you're subtracting?  It's possible and I'll show you how.

In this activity you will hear the mathematical difference between two very similar frequencies.  When two sound waves combine, they momentarily produce louder pulses called "beats."  The key is to hear the "beat frequency" — the number of beats per second.  It's always the difference, or the amount you would get by subtracting the two numbers, e.g., 443 Hertz - 440 Hertz = a beat frequency of 3 Hertz, or 3 pulses per second.

Step 1: Begin by clicking 440 Hz.  What you're hearing is a sound wave vibrating 440 times per second, or 440 Hertz.   In music, we call this "A-440."  It has this name because it's the musical pitch "A" and it's vibrating at 440 Hertz.   This exact pitch is what most symphony orchestras use to tune before a concert — it's also the frequency produced by most tuning forks.
Step 2: Now click 441 Hz and watch the clock.  You will hear a pulse or "beat" occurring one time each second.  Also look at the equation that results: 441 Hz - 440 Hz = 1 Hz.  One Hertz is the beat frequency.
Step 3: Click OFF 441Hz and try another frequency.  In this activity, you can only play two frequencies together.
Step 4: When you're ready, have someone else pick two frequencies.  Close your eyes and listen.  Can you determine the difference between the two numbers being subtracted just by listening?