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

`f=(1)/(2l)sqrt((T)/(pir^(2)rho))=(1)/(l)sqrt((T)/(pid^(2)rho))[becaused=2rand4r^(2)=d^(2)]`
`implies (f_(1))/(f_(2))=(l_(2))/(l_(1))sqrt((T_(1))/(T_(2))xx((d_(2))/(d_(1)))^(2)xx(rho_(2))/(rho_(1)))`
`=(35)/(36)sqrt((8)/(1)xx((1)/(4))^(2)xx(2)/(1))=(35)/(36)`
`f_(2)=(36)/(35)xx360=370,f_("beat")=f_(2)-f_(1)=10`