This Learning Object explores the relationship between wave interference and beats. It also looks at instruments and beat frequencies

1. Beats
&
Balinese Gamelan Orchestras
Caroline Cullinan
"INDONESIAN TRADITIONAL MUSIC." Hz36s Blog. N.p., 18 Feb. 2012. Web. 15
Mar. 2015.

2. When two plane waves with the same wavelength
propagate in slightly different directions, their relative
phase varies with position. At points where the two
waves are exactly in phase, the amplitudes add,
resulting in constructive interference. At points where
the two waves are exactly out of phase, the result is
destructive interference. The regions of constructive
and destructive interference are separated by intervals
of space and also intervals of time.
Beating
by
Wave Interference

3. Hawkes, Robert, Javed Iqbal, Firas Mansour, Marina Milner-Bolotin, and Peter William. Physics for Scientists and
Engineers: An Interactive Approach. Vol. 1. N.p.: Nelson Education, 2013. Print. Revised Custom.

4. When we listen to the two sound waves that have
slightly different frequencies, the alternating
constructive and destructive interference caused by
the increasing an decreasing amplitude as a function of
time produces a beat. The sound alternates between
soft and loud.

5. The rate at which the amplitude varies is proportional to
the frequency difference. However, when the
frequency difference is large, the sound can be heard as
two distinct tones, instead of one tone with a varying
intensity.

6. Hawkes, Robert, Javed Iqbal, Firas Mansour, Marina Milner-Bolotin, and Peter William. Physics for Scientists and
Engineers: An Interactive Approach. Vol. 1. N.p.: Nelson Education, 2013. Print. Revised Custom.

7. In the previous slide, the sound waves interfere
constructively at first. Then, halfway across the graph,
the waves are out of phase and interfere destructively
because the red wave has completed two full cycles and
the blue wave has only completed one and a half cycles.
After two more red wave cycles, the waves are back in
phase. The varying amplitude of the resultant wave
(green wave) creates the beating sound.

8. When the two waves are close in frequency, the resulting tone
has the mean frequency and the amplitude varies by the
difference in angular frequency.
Hawkes, Robert, Javed Iqbal, Firas Mansour, Marina Milner-Bolotin, and Peter William. Physics for Scientists
and Engineers: An Interactive Approach. Vol. 1. N.p.: Nelson Education, 2013. Print. Revised Custom.

9. Hawkes, Robert, Javed Iqbal, Firas Mansour, Marina Milner-Bolotin, and Peter William. Physics for Scientists and
Engineers: An Interactive Approach. Vol. 1. N.p.: Nelson Education, 2013. Print. Revised Custom.

10. Beats are utilized by musicians when determining
whether or not an instrument is out of tune. When
musicians adjust the frequencies of their notes, they
aim to stop the beating sound associated with an out of
tune instrument. In doing this, musical ensembles
ensure that all of the sounds produced by each
instrument are agreeable.

11. Balinese Gamelan groups are unique from typical ensembles. Unlike
most musical groups, a Balinese gamelan orchestra does not use the
standard pitch (in Western classical music A is tuned to a frequency of
440 Hz). Balinese gamelan groups instead use a majority of bronze
percussive instruments that are intentionally out of tune from each
other. Instruments utilized include xylophone-like metallophones that
vary in size and pitch, tuned gong chimes, large pitched gongs, and
drums. Instruments in a Balinese gamelan ensemble are tuned in pairs,
with one instrument tuned higher in pitch than its partner. The
intentional detuning of notes produced by pairs of instruments results in
a “shimmering” effect in the music.
Beats and Balinese Gamelan Orchestras

12. Frequencies of the tones of several
gamelan orchestras in Bali
"Gamelan Bali." Pitch and Tuning of Balinese Gamelan Orchestras. N.p., n.d. Web. 15 Mar. 2015.

13. *Remember: Balinese gamelan orchestra music is intentionally out of tune
Question
One day,

14. *Hint: If two instruments are simultaneously played and
produce detectable beats, then the frequencies are not
identical. Instruments that are perfectly tuned to each
other will reduce and produce a beat frequency of 0 Hz.

15. • First, find the the beat frequencies heard for each combination of bronze
percussion instruments
Solution- Instrument 1 (350 Hz) & Instrument 4 (425 Hz)
Now, look for the combination of two instruments that has the greatest beat
frequency. This combination of the two most detuned instruments produces the
most out of tune sound. Thus, anyone listening to the 6 combinations of beat
frequencies would be able to identify the most out of tune instrument
combination (that with the largest beat frequency) as the combination that best
resembles Balinese gamelan music.

16. Works Cited
"Description Of The Music Of The Balinese Gamelan." « Gamelan Tunas Mekar. N.p., n.d.
Web. 15 Mar. 2015.
"Gamelan Bali." Pitch and Tuning of Balinese Gamelan Orchestras. N.p., n.d. Web. 15 Mar.
2015.
Hawkes, Robert, Javed Iqbal, Firas Mansour, Marina Milner-Bolotin, and Peter William.
Physics for Scientists and Engineers: An Interactive Approach. Vol. 1. N.p.: Nelson
Education, 2013. Print. Revised Custom.
"INDONESIAN TRADITIONAL MUSIC." Hz36s Blog. N.p., 18 Feb. 2012. Web. 15 Mar. 2015.
"Review of Soniccouture Balinese Gamelan, a Sample Library for Kontakt Featuring a
Semara Dana Gamelan." Rekkerdorg RSS. N.p., 14 Apr. 2008. Web. 15 Mar. 2015.