Sinusoidal Waves: An Artifact Analysis

This artifact is primarily based on Sinusoidal waves and how to use and apply this to represent and develop musical notes. In doing so, I had to use a variety of properties of trigonometry for the key aspects in this artifact. Such as, building an instrument and finding out the relationship between sound waves and the sinusoidal representation. Sinusoidal is any graph mainly consisted of either the sine or cosine function. The general formula for Sinusoidal waves is y=Acosfx+C.The height of the wave of this particular function is the Amplitude. It can be written as y=Asinx and y=Acosx, where the absolute value of A is the amplitude. Also in the trigonometric function, the number of cycles it completes in a given interval 2π is the frequency. It can be written as y=Asinfx and y=Acosfx, where the coefficient, f, is known as the frequency. By adding a constant to a sinusoidal graph, a vertical shift occurs. This can be shown in y=Asinfx+C and y=Acosfx+C. Cis the average value of the trigonometric function. Overall this function …show more content…
Usually, the longer the tube, the lower the note. The three valves of the trumpet add lengths of tubing to the instrument to decrease the pitch. The first valve lowers it by a whole tone, then the second by a semitone, and the third by a minor third. For example, the valves are shown here in order to play the notes of the scale.
The first valve extends the trumpet’s tube by 160 mm, the second by 70 mm, and lastly the third by 270 mm. These measurements are just the right distance for changing the pitch by the expected interval. When the trumpet valve is raised, the air goes directly through, and when it is lowered, a different airway is opened which attaches a section of tubing. The distance to add for the three valve intervals is found by using the known information that the frequency of an air column is inversely proportional to