## Beats and Combination Tones

When two sine waves of equal amplitudes but different frequencies are played simultaneously, several interesting sounds can be heard.

• If the two tones have a frequency difference of less than ~10Hz, a single composite tone is heard whose frequency is the average of the two tones.  The composite tone will pulsate, or "beat", in amplitude at a frequency equal to the difference of the two tones.

• As the frequency difference increases, the beats become too fast to count but the composite tone remains "rough".

• If the frequency difference is less than the limit of frequency discrimination, then a "fused", composite tone is heard.

• If the frequency difference is greater than the limit of frequency discrimination, then the two tones will be heard as distinct pitches.

• Tones, called "combination tones", other than the two source tones may be sensed.  Some believe that when combination tones are heard, the ear/brain is recognizing periodic nerve impulses sent when the basilar membrane moves past a critical displacement.  Because the detection of combination tones is strongly dependent on the volume of the tones, others believe that combination tones are due to nonlinear distortion of the sound waves in the eardrum, middle ear, and inner ear.

Primary beats

Play 440Hz sine wave.

The following files plays the sum of two sine waves: one of frequency 440Hz and the other of different frequencies, f2

 f2= 441 Hz 445 Hz 450 Hz 460 Hz

To hear a constant 440 Hz tone combined with a frequency ramp going from 440 to 450 Hz, play this.

To hear the transition from individually detected beats to the rough, fused composite tone, play this.  It is a constant 440Hz tone combined with a ramp from 460 to 485 Hz.

Combination tones

Two tones are presented with equal amplitude.  One remains at the starting frequency of 440Hz.  The other starts at the same frequency and its frequency gradually increases to 880Hz. First play the file with a soft to moderate volume.  Then increase the volume with each repetition.  Do you hear a descending frequency ramp?  The instantaneous frequency of the descending tone is 2f1-f2, where f1 is, in this case, 440Hz.  With an even louder volume, you will hear more frequency ramps in addition to that heard at the starting volume. These are combination tones.  Play it.  To check that the computer sound card and speakers aren't the source of the combination tones, play this ramp without the constant tone at 440Hz.

Stereo beats

• You need to use headphones for this demonstration.

Another interesting phenomenon can be heard when playing a tone of one frequency in one ear and a tone of a different frequency in the other ear.  These are called stereo beats and demonstrate that beats can even be processed in the auditory cortex of the brain. Play 440Hz & 445Hz .  The tone quality should be slightly different than what you heard in the primary beat section.  This is partially due to the brain's ability to localize a sound source.  Try this stereo beat of 440Hz & 450Hz.