Two point sound sources `A` and `B` each to power `25pi w` and frequency `850 Hz` are `1 m` apart. The sources are in phase

(a) Determine the phase difference between the waves emitting from `A` and `B` received by detector `D` as shown in figure.
(b) Also determine the intensity of the resultant sound wave as recorded by detector `D`. Velocity of sound `= 340 m//s`.

Answer

(a) `pi` , (b) `l = (sqrt(l_(A)) - sqrt(l_(B)))^(2) = (25//312)^(2)`

Explanation

(a) `lambda = (340)/(850) Deltaphi = (2pi)/(lambda) DeltaS`
`= (2pi xx 850)/(340) xx [sqrt(1^(2) + 2.4^(2)) - 2.4]`
`= (2pi xx 850)/(340) xx [2.6 - 2.4] = (2pi xx 850)/(340) xx 0.2 = pi`
(b) `l = l_(A) + l_(B) + 2 sqrt(l_(A) + l_(B)) cos pi`
`= (sqrt(l_(A)) - sqrt(l_(B )))^(2) `
`= [sqrt((P)/(4pi(2.4)^(2)))=sqrt((P)/(4pi(2.6)^(2)))]^(2)=[sqrt((25pi)/(4xxpixx(2.4)^(2)))-sqrt((25pi)/(4pi(2.6)^(2)))]^(2)=((5)/(2 xx 2.4) - (5)/(2 xx 2.63))^(2)`
`[(5)/(2)((2.6 - 2.4)/(2.4 xx 2.6))]^(2)=((5)/(2)xx(0.2)/(2.4xx2.6))^(2)=((25)/(12xx26))^(2)=((25)/(312))^(2)`