The Physics of Music: Waves, Beats & Frequencies

Creative endeavors and the hard sciences often go hand in hand. Understanding the physics of sound can lead to an understanding of the physics of music and how aesthetically pleasing sounds and arrangements can be made.

Sound Waves and Frequencies

Sound waves are vibrations in a medium, which can be perceived by the human ear. The frequency of a sound wave is the number of vibrations per second, measured in Hertz.

The fundamental frequency of an object that is producing sound is the lowest natural frequency at which that object will vibrate. The value of this frequency depends on the physical properties of the object.

The frequencies in a harmonic series are whole number multiples of the fundamental frequency; however, it is possible to have overtones (standing wave patterns) at frequencies which are not multiples of the fundamental. A musical scale is a set of musical notes ordered by fundamental frequency.

Human Voice and Singing

In any particular object – whether it be your vocal cords or a musical instrument, standing waves create specific sounds. Your perception of that sound depends on the frequency of vibration, including any lower amplitude overtones that contribute to the timbre, or perceived sound quality.

Humans create music by vibrating the air column in their throats. By changing the shape/tension in their vocal cords, they can create different vibrational modes and sounds. Practiced singers have learned to do this very well and can shape their vocal cords so as to hold a pure note for a long time, as well as hit several exact notes on a musical scale without faltering in pitch.

When people talk about particular music notes, they are referring to certain specific sound frequencies. Higher frequencies create higher notes, and lower frequencies create lower notes.

Musical Instruments

Musical sound can also be created by musical instruments. Pipe organs, woodwinds, saxophones, theremins and other electronic instruments, are all examples, and each one creates musical sound in different ways.

Woodwinds and other similar instruments create sound by vibrating columns of air. By adjusting the lengths of the instruments, or opening and closing holes in the sides, the natural vibrational frequency of the column is changed, producing different notes.

String instruments create sound by producing standing waves on taut strings which are amplified in the body of the instrument. The frequency at which a string will vibrate depends on its mass density, length and tension.

That is why these instruments can be tuned by adjusting the tension of the strings, and why some of the strings are thicker than others. It is also why on an instrument like a guitar, different notes are created by pressing the strings down at the frets – in doing so, you are essentially varying the lengths of the strings.

Other instruments operate on the principle of a vibrating membrane. Drums are a prime example of this. A drum head can be thought of as the two dimensional version of the vibrating string. The frequencies at which it will vibrate when struck depend on its mass density and tension, but because it is a two dimensional membrane, many more possible vibrational modes exist.

Beats and Beat Frequencies

Beats are a phenomenon that result from sound wave interference and have many applications including in musical instruments. If two sound waves of different frequencies interfere, a varying amplitude results from a switch between constructive interference and destructive interference between the two waves. This variation in the loudness of the sound is known as beats.

The beat frequency is defined as the difference in frequency between the two original waves. This means that the closer the two frequencies are, the smaller the beat frequency is (meaning fewer beats per second), which makes them easier to distinguish with the human ear.

Certain beat frequencies are perceived by the human ear as a "subjective frequency" or "difference frequency."

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