Two wires are fixed in a sanometer. Their tension are in the ratio `8:1` The lengths are in the ratio `36:35` The diameter are in the ratio `4:1` Densities of the materials are in the ratio `1:2` if the lower frequency in the setting is `360Hz`. The beat frequency when the two wires are sounded together is

Answer

A, C

Explanation

Given, `T_1/T_2 = 8/1, L_1/L_2=35/36 `
`D_1/D_2 = 4/1, rho_1/rho_2 =1/2 `
Let `mu_1` and `mu_2` be the linear mass densities, then
`:. mu_1 = pi xx D_(1)^2/4 xx rho_1` and `mu_2 = pi xx D_(2)^2/4 xx rho_2`
`:. mu_1/mu_2 = (D_1/D_2)^2 xx rho_1/rho_2 = (4/1)^2 xx 1/2 = 8/1 `
`:. f_1/f_2 = L_2/L_1 xx sqrt (T_1/T_2xxmu_2/mu_1) = 35/36 sqrt((8/1) xx (1/8)) = 35/36 ` , `(f=1/(2L) sqrt(T/(mu))`
` f_2 gt f_1`
We have `f_2 = 360`
`:. f_1= 350` .