Question

Calculate the frequency of the fundamental tone of a 100 cm long wire with 1.8 mm diameter (density 8.4) and stretched by 20 kg weight.

Answer 1

l = 100cm = 1.00m; D = 1.8mm;
∴ r = \(\frac { 1.8 }{ 2 } \) = 0.9mm = 0.9 × 10^-3 m = 9 × 10^-4 m
P = 8.4 × 10³ kg m^-3;
The fundamental tone frequency = ?
Mass of the stretched wire,
m = volume × density = πr².lp
= 3.14 × (9 × 10^-4 m)² × 8.4 × 10³
= 3.14 × 81 × 10^-8 × 8.4 × 10³
= 2136.456 × 10^-5
= 2.1385 × 10^-2
T = Mg = 20 × 9.8 = 2 × 98 N
∴ Fundamental frequency of the wire