Question

how Fourier analysis can be used to study musical instrument on any other device.

Answer 1

Musical Application

Sound waves are one type of waves that can be analyzed using Fourier series, allowing for different aspects of music to be analyzed using this method. Musical instruments produce sound as a result of the vibration of a physical object such as a string on a violin, guitar, or piano, or a column of air in a brass or woodwind instrument. This vibration causes a periodic variation in air pressure that is heard as sound. The period T is the length of time before the signal repeats, and the frequency f1 equal to 1/T is the fundamental frequency or pitch of the note produced. When this vibration occurs in a musical instrument, not only is the frequency f1 produced, but other frequencies are produced as well. These frequencies are integer multiples of the fundamental frequency f1 ,like 2f1,3f1,4f..... The frequency f1 is called the fundamental, and the frequencies f2, f3, f4, etc. are called the harmonics. We call f2 the second harmonic, f3 the third harmonic and so on