The A beat frequency or beat wave is a
sound of fluctuating volume caused when you add two
sound waves of slightly different frequencies. The sound
of a single pitch or tone consists of only one specific
wavelength or frequency, represented in the form of a
sine wave. The volume you hear depends on the amplitude
of the wave. When you add another sound wave of the same
pitch, the new volume will be the sum of the two
amplitudes, provided the waves are in unison or have the
same phase. But if you add two sound waves of slightly
different frequencies, the sound you hear will fluctuate
in volume according to the difference in their
frequencies. These are called beat frequencies or beat
Questions you may have include:
Although sound is a compression wave
that travels through matter, it is more convenient to
illustrate the sound wave as a transverse wave, similar
to how a guitar string vibrates or how a water wave
appears. The shape of such a wave for a single frequency
is called a sine wave.
Obviously, the sound represented by the
sine wave is moving at some velocity v. The number of
peaks or crests that pass by a given point is the
frequency f of the sound wave. The wavelength L is the
distance between crests. (Usually, the symbol for
wavelength is the Greek letter lambda and the symbol for
frequency is nu, but since we don't have those letters
available, we'll use L and f in this lesson.)
The relationship between velocity,
wavelength and frequency is:
v = L x f
The pitch or tone of a sound is usually
represented by its frequency.
The unit of measurement for velocity is
in distance/time, such as meters/second. The unit for
wavelength is distance, such as meters. The unit for
frequency relates to 1/time.
NOTE: Frequency used to be designated as
cycles per second (cps). But in the 1960s they changed
the name to Hertz (Hz) to honor scientist Heinrich
Hertz. This change from a logical to something obscure
also confused millions of students.
A good test is to check the units in the
meters/second = L meters x f 1/second =
This is to assure you aren't mixing your
units of measurement.
The amplitude of the sine wave is its
height. Some measure the amplitude from peak to peak,
while others measure it from the center to the peak. The
amplitude represents the volume of the sound.
If you add two waves of the same
wavelength or same frequency, and they are in unison or
the same phase, the amplitudes will add. But it you add
two waves of slightly different frequencies, the
resulting amplitude will vary or oscillate at a rate
that is the difference between the frequencies. That
beat frequency will create a sine wave envelope around
the original sine wave.
Sum of two waves creates beat frequency
For example, if you add a wave
oscillating at 440 Hz with one that is at 445 Hz, the
resulting frequency will be an average of the two, and
its volume will oscillate at the beat frequency of 5 Hz.
If you add 440 Hz and 500 Hz notes, the
resulting waveform will not be a pure sine wave.
Instead, it will be a complex version of a sine wave and
will sound like a blurred average of the two tones.
Also, its beat frequency will be 60 Hz, which would
sound like a very low-pitched hum instead of a
You have assumed that the beat frequency
is given by A-B, whereas surely it's actually (A-B)/2,
as in ...
Sin(A) + Sin(B) = 2.Cos[(A-B)/2].Sin[(A+B)/2]
In support of this, you can roughly time
the period between low points with the green button of
your demo, it's nearer to 2 secs (0.5 Hz) than 1 sec (1
So I think the beat frequencies printed
in your text should be halved.
A piano tuner will strike a key and then
compare the note with a tuning fork. If the piano is
slightly out of tune, he will be able to hear the beat
frequency and then adjust the piano wire until it is at
the same frequency as the tuning fork. If the piano is
severely out of tune, it makes the job more difficult,
because the beat frequency may be too fast to readily
When you fly in a passenger plane, you
may often hear a fluctuating drone. That is a beat
frequency caused by engine vibrations at two close
Often you will hear the voice of a
singer fluctuate with a vibrato. Singing two notes very
close to each other cause this beat frequency.
A beat frequency is the combination of
two frequencies that are very close to each other. The
sound you hear will fluctuate in volume according to the
difference in their frequencies. This can be graphically
shown as a sine wave that has an envelope consisting of
another sine wave at a larger wavelength. You may hear
beat frequencies when objects vibrate.