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BEATS
DEFINITION:
When two sound
waves of different
frequency
approach your ear,
the alternating
constructive and
destructive
interference causes
the sound to be
alternatively soft
and loud
• Loud-soft-loud modulations of
intensity are produced when
waves of slightly different
frequencies are superimposed.
• The beat frequency is equal to
the difference frequency |f
1
-f
2
|
Superimpose oscillations of equal amplitude, but
different
Frequencies:
Asin(2π f 1t) + Asin(2π f2 t)
=2Asin(2π (f1 + f2)t/2)cos(2π (f1 − f2)t/2)
= 2Acos(2π ( f1 − f2 ) t/2) sin(2π ( f1 + f2 ) t/2)
Modulation of amplitude Oscillation at the average frequency
BEATS
Since the frequencies of the two sounds are
so close:
you would hear a sound that is an average
of the two.
you would also hear the modulation of the
amplitude as a beat frequency, which is the
difference between the initial frequencies:
fb = | f1 − f2 |
Examples of beat frequencies:
• A pure sound of 330 Hz is combined with 331
Hz to give a rather slow beat frequency of 1
Hz or 1 fluctuation in amplitude per second.
• When the 330 Hz sound is combined with a
340 Hz sound, you can hear the more rapid
fluctuation at 10 Hz.

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Beats lo8

  • 2. DEFINITION: When two sound waves of different frequency approach your ear, the alternating constructive and destructive interference causes the sound to be alternatively soft and loud
  • 3. • Loud-soft-loud modulations of intensity are produced when waves of slightly different frequencies are superimposed. • The beat frequency is equal to the difference frequency |f 1 -f 2 |
  • 4. Superimpose oscillations of equal amplitude, but different Frequencies: Asin(2π f 1t) + Asin(2π f2 t) =2Asin(2π (f1 + f2)t/2)cos(2π (f1 − f2)t/2) = 2Acos(2π ( f1 − f2 ) t/2) sin(2π ( f1 + f2 ) t/2) Modulation of amplitude Oscillation at the average frequency
  • 5. BEATS Since the frequencies of the two sounds are so close: you would hear a sound that is an average of the two. you would also hear the modulation of the amplitude as a beat frequency, which is the difference between the initial frequencies: fb = | f1 − f2 |
  • 6. Examples of beat frequencies: • A pure sound of 330 Hz is combined with 331 Hz to give a rather slow beat frequency of 1 Hz or 1 fluctuation in amplitude per second. • When the 330 Hz sound is combined with a 340 Hz sound, you can hear the more rapid fluctuation at 10 Hz.