Is there such a thing as sound in Trigonometry? We hear because of vibrations that send pressure waves to our ears. These waves send a message to our brain about the amplitude and frequency and we hear sound. The frequency is the rate in which a vibration occurs that constitutes a wave. We have a mathematical picture of frequency of oscillation which describes the oscillation that occur so many times per second. The graph of a sine function is one cycle in one second has a sideways “S” shape. We measure that oscillation in Hertz or cycles per second. When sound is generated by a speaker electricity, and a cone attached to electromagnet is used to make the cone oscillate back and forth to produce sound. The number of times that the cone oscillates corresponds to a pure note like A. The chromatic scale increases the frequency of oscillation by 12 steps from one octave to another. “Starting at A 440, the frequencies of the chromatic scale would be 440*20, 440*2 1/12, 440-2 2/12…440*2 12/12=880.” “Each of the notes in between has a name of its own; they are: A, A#, B, C, C#, D, D#, E, F, F#, G, G#, A2.” Once you get the notes then you can add a chord which is playing multiple notes at once. You can do this by using multiple speakers next to each other making them oscillate at the correct frequency. The mathematical function for a chord is: “sin (440 2t), sin (440 24/12 2t), sin (440 27/12 *2t)” “For a louder or softer note you can multiply the whole function by a constant to increase or decrease the volume of that note.” “Now with the use of computers we can more easily balance sound.” Many different computer programs are used to make different sound waves and different types of graphs. The graphs are recorded and trigonometric equations are used to calculate to enhance a singer’s voice and what we ultimately hear when we are listening to music. Engineers also use trigonometry to calculate angles of waves in order to design a studio or concert hall. They will install special panels on the walls so that sound will bounce off of the wall at specific angles to get the correct sound waves.