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. `5s^(-1)`
B. `10s^(-1)`
C. `15s^(-1)`
D. `20s^(-1)`

Answer

B

Explanation

Here, `(T_(1))/(T_(2))=(8)/(1),(l_(1))/(l_(2))=(36)/(35),(D_(1))/(D_(2))=(4)/(1),(rho_(1))/(rho_(2))=(1)/(2),`
`v_(2)360s^(-1)`
As, `v=(1)/(lD)sqrt((T)/(pirho)),`
So, `(v_(1))/(v_(2))=(l_(2)D)/(l_(2)D)sqrt((T_(1))/T_(2)xx(rho_(2))/(rho_(1)))=(35)/(36)xx(1)/(4)sqrt((8)/(1)xx(2)/(1))=(35)/(36)`
`:. v_(1)=(35)/(36)xx360=350s^(-1) ,`
Frequency of beats `=v_(2)-v_(1)=360-350=10s^(-1)`