Primary 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.

Two tones are presented with equal amplitude.  One remains at the starting frequency.  The other starts at the same frequency and its frequency gradually increases.  Three frequency excursions of differing lengths are possible.

Starting frequency [Hz] (default is A above middle C)

MUTE

Beats with constant frequency shift:     Df = 1 Hz     Df = 5 Hz     Df = 10 Hz

Two tones are presented with equal amplitude.  One remains at the starting frequency.  The OTHER starts at the same frequency and its frequency gradually increases.  Three frequency excursions of differing lengths are possible.

Short Ramp (Primary beats)     Medium Ramp (Roughness)     Wide Ramp (Combination tones)

Above figure for two pure tones is from Rossing, Moore and Wheeler, 3rd edition. This demonstration was created by Dan Boye using the Java2 sound interface written by Todor Penev.