individual flutes, especially where they are handmade. Head joint geometry appears particularly critical to acoustic performance and tone, but there is no clear consensus on a particular shape amongst manufacturers. Acoustic impedance of the embouchure hole appears the most critical parameter. Critical variables affecting this acoustic impedance include: chimney length (hole between lip-plate and head tube), chimney diameter, and radiuses or curvature of the ends of the chimney. Generally, the shorter the hole, the more quickly a flute can be played; the longer the hole, the more complex the tone. Finding a particularly good example of a flute is dependent on play-testing. Head joint upgrades are usually suggested as a way to improve the tone of an instrument. Cheaper student models may be purchased with a curved head to allow younger children with shorter arms to play them. Tubing materials Less expensive flutes are usually constructed of brass, polished and then silver-plated and lacquered to prevent corrosion, or silver-plated nickel silver (nickel-bronze bell metal, 63% Cu, 29% Zn, 5.5% Ni, 1.25% Ag, .75% Pb, alloyed As, Sb, Fe, Sn). Flutes that are more expensive are usually made of more precious metals, most commonly solid sterling silver (92.5% silver), and other alloys including French silver (95% silver, 5% copper), "coin silver" (90% silver), or Britannia silver (95.8% silver). It is reported that old Louis Lot French flutes have a particular sound by nature of their specific silver alloy. Gold/silver flutes are even more expensive. They can be either gold on the inside and silver on the outside, or vice versa. All-gold and all-platinum flutes also exist. Flutes can also be made out of wood, with African blackwood (grenadilla or Dalbergia melanoxylon) being the most common today. Cocuswood was formerly used, but this is hard to obtain today. Wooden flutes were far more common before the early 20th century. The silver flute was introduced by Boehm in 1847, but did not become common until later in the 20th century. William S. Haynes, a flute manufacturer in Boston, Massachusetts, United States, told Georges Barrère that in 1905 he made one silver flute to every 100 wooden flutes, but in the 1930s, he made one wooden flute to every 100 silver flutes. Unusual tubing materials include glass, carbon fiber, and palladium. Professionals tend to play more expensive flutes. However, the idea that different materials can significantly affect sound quality is under some contention, and