Two sound sources `S_1 and S_2` emit pure sinusoidal waves in phase. If the speed of sound is 350 m/s,
(a) For what frequencies does constructive interference occur at P?
(b) For what frequencies does destructive interference occur at P?

Explanation

Path difference `Delta x = S_1P - S_2P`
`=sqrt((2)^2 +(4)^2) - sqrt((1)^2 + (4)^2)`
`=4.47 - 4.12 = 0.35m`
(a) Constructive interference occurs when the path difference is an integer number of wavelength.
`or Deltax = nlambda = (xv)/(f) or f = (n (v))/(Deltax)` where n = 1,2,3 ......
`:. f = (350)/(0.35), (2 xx 350)/(0.35), (3 xx 350)/(0.35),`.......
`f = 1000Hz, 2000 Hz, 3000 Hz,...,` etc.
(b) Destructive interference occurs when the path difference is a half-integer number of wavelengths
`Deltax = (2 n +1) lambda/2 n =0, 1,2,...(or ) Deltax = (2n +1) v/(2f)`
`:. f = ((2n +1)v)/(2Deltax) =350/(2 xx 0.35) , (3 xx 350)/(2xx 0.35) , (5xx350)/(2 xx 0.35)`......
= 500 Hz, 1500 Hz, 2500 Hz