The document discusses how beat frequencies help musicians tune their instruments. It explains that when two sounds of different frequencies are played together, the listener hears an alternating loud and soft pattern called a beat frequency. Musicians tune their instruments by adjusting the frequency to eliminate this beating. The document provides examples of calculating the tone and beat frequency that would be heard when different instruments play an A note together before and after tuning. It demonstrates how beat frequencies allow musicians to perfectly tune their instruments.

1. The Principle Violinist – An
Application of Beat Frequency

2. The pit orchestra is in place. The principle violinist
enters and bows. She plays her open A string and
brings to life all the instruments around her, as they fall
together in melodic cohesion. One by one they drop
out as they find their tuning. The conductor taps his
baton to catch the attention of his brigade and with the
first flick of his wrist, they begin.
As poetic as this sounds, there is actually a very
interesting physics application to this.

3. • At 440 Hz, the frequency of a properly
tuned violin A-string, it is easy for the
human ear to pick up deviations from this
tuning. These deviations are heard
through beat frequencies.

4. • Beat frequencies are caused by the
combination of constructive and
destructive interference that happens
when there are two sounds of different
frequencies interacting. This causes the
listener to hear an alternating loud
(constructive interference) and soft pattern
(destructive interference).

5. • Musicians tune by tightening or loosening
their strings, or changing the length of the
pipe by pulling apart or pushing together
pieces of the instrument. By doing this
they are altering the frequency, and
(hopefully) eliminating the beating.

6. Tone vs Beat Frequency
• The tone can be found by averaging the two
frequencies = (f1+ f2)/2. While tuning, the
musicians are looking for the purest tone
possible.
• The beat frequency can be found by
subtracting one frequency from the other
=| f1-f2| . While tuning, musicians are
trying to eliminate the beat frequency, to
give a pure tone.

7. Test your knowledge
• Two violinists want to play a duet in perfect
harmony. The first violinist plays his open A
string. It has a frequency of 444 Hz. The
second violinist plays his open A string and it has
a frequency of 449 Hz.
• A) What is the tone that a listener hears when
the two violinists play their A strings together
before tuning?

8. • B) What is the beat frequency that a
listener hears when the two violinists play
their A strings together before tuning?

9. • C) The second violinist tunes his A string
to the first violin. They decide to add a
pianist for a more full sound. The piano is
perfectly in tune, and plays an A at 440 hz.
Now what is the tone heard when the
pianist plays her A at the same time as the
first violinist?

10. • D) What is the beat frequency heard when
the piano and the first violin play A at the
same time?

11. Answers
• We have the following formulas to use:
• Tone = (f1+ f2)/2. beat frequency = |f1-f2|
• A) (444+449)/2 = 446.5 Hz
• B) 449-441 = 5 beats per second
• C) (444+440)/2 = 442 Hz
• D) 444-440 = 4 beats per second

12. Thanks for watching!

13. Bibliography
• http://hyperphysics.phy-
astr.gsu.edu/hbase/sound/beat.html
• https://www.youtube.com/watch?v=-
YtJJFAZzlU