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

Options

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

Answer

C

Explanation

`n=(1)/(2l)sqrt((T)/(m))=(1)/(2l)sqrt((T)/(pir^(2)rho))=(1)/(2lr)sqrt((T)/(pirho))`
`(n_(1))/(n_(2))=(l_(2))/(l_(1))*(r_(2))/(r_(1))*sqrt((T_(1))/(T_(2)))*sqrt((rho_(2))/(rho_(1)))=(35)/(36)*(1)/(4)*sqrt((8)/(1))*sqrt((2)/(1))=(35)/(36)`
Higher frequency `n_(2)=360`
`therefore n_(1)=(35)/(36)xx360=350`
`therefore` No. of beats/sec=360-350=10.