A piano wire has a length of 81 cm and a mass of 2.0

g. if its fundamental frequency is to be 394 hz, its tension must be

Frequency = 394 Hz

Length of the string L = 81 cm = 0.81 m

Mass of the string = 0.002 kg

Tension T = ?

Wave length of the string is two times the length.

n x lambda = 2L, we also have lambda = vt = v / f, t is time period and given n = 1.

Therefore L = v / 2f = > v = 2fL

Deriving form force equation, force here is tension T so

v = squareroot of (TL/m) hence

2fL = squareroot of (TL/m) = > 4 x f^2 x L^2 = (T x L) / m = > T = 4 x f^2 x L x m

T = 4 x 0.81 x (394) ^2 x 0.002 = 4 x 0.81 x 155236 x 0.002

T = 1005.9 N = 1.006 x 10^3 N