physics behind the piano
...ith a different type of metal with much less tension. This high-tension string not only demands a heavier hammer and a sturdier action, but a very strong structure, consisting of the pin block, plate, and back posts. The string is strung from a steel pin driven into a laminated block of hardwood, stretched across the plate and over the bridge and around a hitch pin at the other end of the cast iron plate. The combination of the pin block, plate, and back posts support the tension of the strings, and are crucial to tuning stability and the length of serviceability of the instrument. Physics behind the Piano The piano has 88 keys, and its notes span a frequency range from the low A0 (27.5 Hz) to the high C8 (4186 Hz). The 10 lowest notes have single strings, the next 18 notes have two strings each, and the remaining notes have 3 strings. The total tension of the tuned strings can be as high as 60,000 lbs in a concert grand piano. The need for this support is a large part of the reason for the cast-iron frame. -Action: The notes of the piano result from a felt hammer hitting the string. All of the wooden hardware connecting the keys of the piano to the hammers is called the "action," consisting of many parts (up to 7000 separated pieces, or about 80 per key. When the hammer is set into motion, the damper is lifted from the strings. Just before the hammer is to hit the string, the mechanism "lets go" of the hammer and it hits the string freely (as if it were "thrown" at the string). After it bounces off the string, it is caught by the backcheck, held fairly close to the string, allowing another note to be hit very soon after the first. In this fashion, notes in rapid succession are possible with the piano. -Inharmonicities: The piano strings are stiff, and therefore do not abide strictly by the harmonic formula applying to strings discussed earlier, i.e. where L is the string's length, T is the tension in the strings, and d is the linear mass density. Instead, since the stiffness makes the string snap back to its equilibrium position a little faster, the frequencies are slightly higher than this formula would predict. This "inharmonicity" effect is more pronounced for the higher harmonics (they are more correctly "overtones" and they become sharper and sharper as their frequency increases). -Attack and decay: When a hammer strikes the string, energy is transferred to the string(s) in a sudden, percussive fashion. From then on, the vibration die...