Two sonometer wires A and B are fixed on a sonometer. The ratio of their lengths, diameters, densities and tensions are given below: l A l B = 36 35 ; d A d B = 4 1 ; T A T B = 8 1 ; ρ A ρ B = 1 2 If the higher frequency among the two wires is 360 Hz , then what is the beat frequency (in Hz ) observed when the two wires are sounded together?

Step-by-step solution

Frequency of sonometer wire is given by υ = 1 2 l T m = 1 2 l T πr 2 ρ υ 1 = 1 2 l 1 T 1 πr 1 2 ρ 1 υ 2 = 1 2 l 2 T 2 πr 2 2 ρ 2 υ 1 υ 2 = l 2 l 1 T 1 T 2 × r 2 2 r 1 2 × ρ 2 ρ 1 υ 1 υ 2 = 35 36 8 1 × 1 16 × 2 1 = 35 36 Since υ 1 < υ 2 , this means υ 2 = 360   Hz Therefore, υ 1 = 360 × 35 36 = 350   Hz f beat = υ 2 - υ 1 = 10   Hz