Beautiful Music and the Laws of Physics

by Rebecca Guerreso, AP Physics 1 Student

Ludwig van Beethoven once proclaimed, “Music is … A higher revelation than all Wisdom & Philosophy.” Music plays an important role in many people’s lives, yet few know that the basis of music and its sound derive from the laws of physics. Upon hearing a stirring piano solo, one may wonder what is occurring inside the piano that results in such a beautiful sound; the mysteries of sound within a piano originate from basic physics principles. Physics phenomenon regarding waves and oscillations result in the piano creating music.

Understanding the cause of the diverse sounds a piano produces, requires knowledge of the different parts inside the instrument. When a key is pressed on the piano, a sound is heard; when the key is pressed with a larger amount of force, the sound becomes louder. This sound and its amplitude are caused by four major components of the piano: the hammer, the damper, strings, and the soundboard. Every key has a damper, hammer, and either one, two, or three strings. Each of these parts has a different function; the damper stops the string from vibrating to ensure that when a key is pressed, only that key makes a sound. The hammer strikes the string, resulting in vibrations. The soundboard amplifies the string’s vibrations to make the sound louder. When a key is pressed, the damper is released so that the string can make a sound, the hammer strikes the string, and the string vibrates to make a sound.

A typical piano contains eighty-eight keys and has a range of seven different octaves. Starting from the right side of the piano, the first key has the highest pitch, and the pitch of each key after it decreases. The properties of the string for each key determine the pitch that the key will produce. Physics principles have determined that a longer string results in a lower pitch because the fundamental frequency is equal to the quotient of the velocity and two times the length, f = v/(2L). Inside the piano, the strings increase in length for keys with lower pitches, but if only the length were changed for each string, then the strings would exceed the height of the piano. Therefore, to lower a pitch of a key, the length is increased along with the diameter of the string. This concept holds true for all keys to the right of middle C; the keys to the left of middle C must be adjusted differently. If the diameter and length continued to increase, the string would not be able to vibrate regularly after a certain point, which would result in the production of an irregular sound. The keys to the left of middle C have a very low pitch; to accommodate this low pitch, the normal steel wires are wound with a copper wire. By winding the strings together, the total mass of the string increases, allowing the string to vibrate properly because if the mass is increased then the frequency of the string decreases. These physics principles result in octaves on musical instruments; physics has proven that doubling the length of the string decreases the resulting sound by an octave.

Typically, the frequency of each string on a piano ranges from sixteen hertz to seven thousand and nine hundred hertz, while wavelength varies from four centimeters to two thousand and one hundred centimeters. The ranges in frequencies and wavelengths cause each key to produce a different sound. A piano contains seven octaves and these seven octaves repeat throughout the eighty-eight keys on the piano (first key on far left is A; last key on far right is C). Each note on the piano has a fundamental frequency; to increase the note by one octave, the fundamental frequency must be doubled; to increase the note by two octaves, the fundamental frequency must be quadrupled (or the first level frequency must be doubled). The changed frequency creates different tones for each note.

Another factor that affects the piano’s sound are the three pedals. On a standard upright piano, the pedal farthest to the right is called the damper pedal, and is the most commonly used pedal. This pedal allows the notes to be played much more smoothly. When the damper pedal is pressed, the dampers are released from the strings. Consequently, when a note is played all the strings vibrate since there are no dampers to inhibit vibrations. The celeste pedal is the middle pedal; it drops a felt pad onto the tops of the strings in order to lower the amount of vibrations on the string, and in effect, make the sound much quieter. The pedal to the far left is the una corda pedal; it shifts the hammers so that it strikes fewer strings than usual, creating a softer sound because there are less vibrations.

The piano and the sounds it produces utilize many physics principles. The strings within the piano operate at different frequencies, which result in different wavelengths; this is why the piano has the ability to produce such a vast range of notes. Pianos go “out of tune,” meaning the keys produce incorrect sounds, throughout the year because the temperature fluctuates, which slightly changes the speed of sound in air. The sounds the piano creates is a language that everybody in the world can understand—sounds created by manipulating laws of physics. Henry Wadsworth Longfellow once marveled, “Music is the universal language of mankind,”and I could add physics makes music possible.

Works Cited

Joyner, Lauren, Erika Littman, Emily Massey, and Johanna Robertson. “Piano Physics.” String Vibration. N.p., 2009. Web. 09 May 2016.

Rack, C. Mckinney And Nsf. “Physics of the Piano.” Physics of the Piano N Giordano — Purdue University (n.d.): n. pag. Web. 9 May 2016.

Suits, B. H. “Frequencies of Musical Notes, A4 = 440 Hz.” Frequencies of Musical Notes, A4 = 440 Hz. Michigan Technolgical University, 1998. Web. 09 May 2016.

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