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

Options

A. `5`
B. `8`
C. `6`
D. `10`

Answer

D

Explanation

`(T_(1))/(T_(2)) =(8)/(1), (l_(1))/(l_(2)) = (36)/(35), (r_(1))/(r_(2)) = (4)/(1), (rho_(1))/(rho_(2)) = (1)/(2)`
`(f_(1))/(f_(2)) = (l_(1))/(l_(2)) sqrt(T_(1)/(T_(2))(rho_(2))/(rho_(1)).(r_(2)^(2))/(r_(1)^(2)))`
`= (35)/(36)sqrt((8)/(1).(2)/(1).((1)/(4))^(2)) = (35)/(36)`
`f_(1) gt f_(2), f_(2) = 360`
`f_(1) = (360 xx 36)/(35) = 370`
Beat frequency `= f_(1)-f_(2) =10 Hz`