Two wires are fixed in a sonometer. Their tensions are in the ratio 8:1. The lengths are in the ratio 36:35. The diameters are in the ratio 4:1. Densities of the materials are in the ratio 1:2. If the higher frequency in the setting is 360 Hz, the beat frequency when the two wires are sounded together, is

Step-by-step solution

Frequency of sonometer wire is given by v = 1 2 l T m = 1 2 l T π r 2 p v 1 = 1 2 l 1 T 1 π r 1 2 ρ 1 v 2 = 1 2 l 2 T 2 π r 2 2 ρ 2 ∴ v 1 v 2 = l 2 l 1 T 1 T 2 × r 2 2 r 1 2 × ρ 2 ρ 1 v 1 v 2 = 35 36 8 1 × 1 16 × 2 1 ∵ v 1 < v 2 a n d v 2 = 360 H z Therefore, v = 360 × 35 36 v 1 =350 Hz So, number of beats produced = v 1 - v 2 =360-350=10