Sound Waves In Music

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Recommended: Mathematics in music introduction

Astronomer Galileo Galilei observed that the entire universe “is written in the language of mathematics.” As an avid musician, I chose to study the topic of how math applies to music, more specifically how sound waves are transmitted. My passion for music urged me to research the sounds that are made and how they are produced.
Music is transmitted through sound waves, which are very similar to the sine waves studied in Trigonometry. The differences in the waves result in a different sounds that are transmitted. Vibrating objects travel through a medium (the material that the disturbance is moving through) to create sounds at a given frequency. The frequency is how often the particles vibrate when a wave passes through the medium. The unit that is most used to measure frequencies is the Hertz (Hz) and 1 Hz is equivalent to 1 vibration per second. The frequency affects the pitch of the note that is being played; The higher the frequency the higher the pitch and the lower the frequency the lower the pitch.
Amplitude is the amount of energy that is carried by the wave. In music, the energy is expressed in volume. The amplitude directly affects the volume of the note that is being played. The higher the amplitude, the more energy being carried, the louder the note that is being played. The lower the amplitude, the less energy being carried, the lower the volume of the note being played. The most commonly used unit of measurement for amplitude is the decibel.

A sine wave, also known as sinusoid is the graph of the sine function in trigonometry. The sine function is typically expressed as Y= A sin (B(x-C)) + D.
The amplitude, or A in the equation is 1/2 |max-min| of the height of the graph.
The period of the graph is the horizo...

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... is different every time a different chord is played, shown by the graphs above.The math, including the ratios show which notes will go with each other perfectly and which ones will not be so attractive to one’s ears.To better my research of how math relates to music, I would have to go into better detail seeing how the waves would look in a different key, or on a different instrument. One problem I had while doing this was that I could not find many formulas to figure out how to answer my question without using a graph. While doing this project I came across a quote that I really enjoyed “It is perhaps even more surprising that music, with all its passion and emotion, is also based upon mathematical relationships. Such musical notions as octaves, chords, scales, and keys can all be demystified and understood logically using simple mathematics.” (Plus. Math. org)

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