Sound can be defined as mechanical vibrations transmitted through an elastic medium, traveling approximately 343 m/s in air at 20°C
When vibrations occur, sound waves pass through a medium such as air and cause a disturbance to the particles of the medium.
The amount of particles to vibrate for a given time is known as the frequency (f).
Frequency is measured in units of Hertz (Hz):
1 Hertz = 1
vibration/second
When a musical
pitch is played on a stringed instrument, a certain
frequency is received by the ear. The musical note
heard when the string is sounded is known as the fundamental frequency.
The fundamental frequency of the disturbance is
Because the linear density is a property
of the medium, a fatter string would have a larger
value of
μ than
This affects the frequency because normally, to reduce the frequency by one musical octave, one would have to double the length of the string (to increase the frequency one musical octave, decrease the length by half). However, this relationship is not practical when it comes to the piano! Because the range of frequencies a piano covers is much wider than other stringed instruments, a piano must be tuned to the correct frequency by a combination of changing the linear density and the length of the strings. Therefore, wound strings (typically a steel core with copper windings) are used to not only increase linear density, but to minimize string stiffness. This allows the piano to range from 27.5 Hz (A0) to 4186 Hz (C8) with 88 keys.
The fundamental frequency of the disturbance is
- v is the wave speed on a stretched string
- L is the length
- Ts is the tension of the string
-
μ is the linear density
This affects the frequency because normally, to reduce the frequency by one musical octave, one would have to double the length of the string (to increase the frequency one musical octave, decrease the length by half). However, this relationship is not practical when it comes to the piano! Because the range of frequencies a piano covers is much wider than other stringed instruments, a piano must be tuned to the correct frequency by a combination of changing the linear density and the length of the strings. Therefore, wound strings (typically a steel core with copper windings) are used to not only increase linear density, but to minimize string stiffness. This allows the piano to range from 27.5 Hz (A0) to 4186 Hz (C8) with 88 keys.