النغمات الموسيقية - الصوت .. الفيزياء

Musical notes - Sound .. Physics

Musical notes

We usually judge a sound as musical or not according to the feeling it leaves in the brain. Musical notes are characterized by three specific properties: loudness, pitch, and timbre.

Loudness is a feeling, and therefore it varies from person to person, and increases or decreases as the sound intensity increases or decreases. It is worth noting that the sound intensity is related to the square of the vertical displacement of the wave - i.e. its amplitude - and that the more the source energy spreads in the surrounding medium, the smaller the sound vibrations and the lower the value of its loudness.

The pitch of the note is related to its frequency value N only, and is determined, in stringed instruments, according to the length of the string L, the tension force in it Sh, and the mass of the unit length in it K according to the following equation N = Sh / 052 An example of this is the piano, which produces low frequencies by long, thick strings, and high frequencies by its short, thin strings. It is worth noting here that the tuning of a stringed instrument is done either by tightening the string or by loosening it. As for wind and brass instruments, the frequency of the tone is determined according to the length of the air column, which is changed by the holes or by pressing the tone adjustment tools.

The musical tone is limited to one frequency only, but is usually colored by other frequencies. Each special tone has a fixed frequency called the fundamental frequency N or the first harmonic, accompanied by other frequencies called higher harmonics, whose value is twice 2 N and three times 3 N, etc., the value of the fundamental frequency. If we pluck a thin, flexible string and fix it at its ends, it begins to vibrate and a wave is formed in it that travels in the direction of its length until it reaches one of its fixed ends, then it is reflected and returns in the opposite direction, and the fundamental frequency in this case is accompanied by a wave whose shape consists of a single closed loop. However, if the string vibrates at a frequency that is double the states, its waveform consists of two closed loops. The third harmonic causes a vibration consisting of three rings, and so on.

(The air vibrates at the open end of the tube and the wave amplitude reaches its maximum value. As for its closed end, the air is unable to vibrate and the wave amplitude in it is zero. All harmonics are present in the open tube at both ends (lower image), but an odd number of them are present if the tube is closed at one end and open at the other (upper image).

(On the opposite page) The harmonics present with the fundamental frequency give the musical tone a special character.

The number of higher harmonics present in the tone and the intensity of each of them differ from one instrument to another. The notes produced by a certain instrument are characterized by a known and specific bell. The guitar produces harmonics whose intensity is doubled relative to the previous one, and the piano produces harmonics of the same intensity. As for the fixed bell in the violin, it is produced by the strength of its third harmonic despite the presence of the fourth harmonic.

The total waveform is usually obtained, at any moment, by adding all the amplitudes of the harmonics that make them up at the same moment.

This is known as By the law of superposition, which is applied in the study of both sound waves and electromagnetic waves.

Musical tones are countless. Each one of them has a special and distinctive frequency. When we tune a certain instrument, we select a specific group of these frequencies. It is worth noting that the acceptable musical interval is not determined by the frequencies of the two specific tones, but is closely related to the ratio of their frequencies. In the past, man used a number of diverse musical scales to tune his musical instruments. Today, the common method is to use the reduced equivalent scale, in which the frequency of the octave of the tone is a multiple of the frequency of the tone itself - i.e. equal to its second harmonic - and the frequency of each semitone of the twelve tones between the tone and its octave is in the ratio 12/root 2 = 1.095.
The first through sixth harmonics are often the same as the known chord notes, and the proof of this is that the ear likes to hear them if they are all played at the same time. However, some of the higher harmonics, such as the seventh and ninth, are not always accompanied by notes of the same musical scale, and therefore they are not pleasing to the listener if played alongside the harmonics. For this reason, musical instruments are designed in such a way that the first six reduce the importance of these higher harmonics to the greatest possible degree.

(Frequency range in different musical instruments).