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Cathrina Kothman, Tess Grimaldi, Helena
Carlson
February 2014
•

When sounds are produced,
mechanical energy travel through
air in different wavelengths.

•

Different wavelengths hit our ear in
differing frequencies.

•

Frequencies: the rate in which
different wavelengths travel
through the air (in this case, into
our ear).

b
y = a sin (bx+c) determines the frequency
(the rate in which the wavelengths are traveling through the air)
Frequencies are measured in the unit of Hertz (Hz).
Frequency depends on the number of periods (length of wave)
over time.
• The more periods per unit of time, the higher the frequency
• Higher frequencies equals higher pitch to the ear
• Lower frequencies equals lower pitch to the ear
•
•

y = a sin

Increase b = higher frequency
Decrease b = lower frequency
(bx+c)
•

Chords/combinations are more appealing when
frequencies...
•
•

•

are similar
have wave cycles that match up at
regular intervals (match on x-axis)

Note combinations with wavelength cycles that
do not match up in a pattern will create
dissonant sounds (less pleasing to the ear).
Consonant

Dissonant
•

Pressure comes from the
constant movement of sound
particles

•

In the ear, pressure constantly
fluctuates up and down

•

Compressions: the high
pressure points of a sound
wave

•

Rarefactions: the low pressure
points of a sound wave

•

Rate of compressions and rarefactions indicates pressure

•

Rate of compression-rarefaction is proportional to
frequency
•

Humans and animals can distinguish the
different frequencies/fluctuations of
sound/pressure waves.

•

Infrasound: Vibrations lower than
human range (less than 20 Hz)

•

Ultrasound: Vibrations higher than
human range (more than 20,000Hz)

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Musica mathematics

  • 1. Cathrina Kothman, Tess Grimaldi, Helena Carlson February 2014
  • 2. • When sounds are produced, mechanical energy travel through air in different wavelengths. • Different wavelengths hit our ear in differing frequencies. • Frequencies: the rate in which different wavelengths travel through the air (in this case, into our ear). b y = a sin (bx+c) determines the frequency
  • 3. (the rate in which the wavelengths are traveling through the air) Frequencies are measured in the unit of Hertz (Hz). Frequency depends on the number of periods (length of wave) over time. • The more periods per unit of time, the higher the frequency • Higher frequencies equals higher pitch to the ear • Lower frequencies equals lower pitch to the ear • • y = a sin Increase b = higher frequency Decrease b = lower frequency (bx+c)
  • 4. • Chords/combinations are more appealing when frequencies... • • • are similar have wave cycles that match up at regular intervals (match on x-axis) Note combinations with wavelength cycles that do not match up in a pattern will create dissonant sounds (less pleasing to the ear).
  • 6. • Pressure comes from the constant movement of sound particles • In the ear, pressure constantly fluctuates up and down • Compressions: the high pressure points of a sound wave • Rarefactions: the low pressure points of a sound wave • Rate of compressions and rarefactions indicates pressure • Rate of compression-rarefaction is proportional to frequency
  • 7. • Humans and animals can distinguish the different frequencies/fluctuations of sound/pressure waves. • Infrasound: Vibrations lower than human range (less than 20 Hz) • Ultrasound: Vibrations higher than human range (more than 20,000Hz)