Two sources are placed from a person `P` as shown in figure. The speed of sound in air is `320 m//s`.
(a)
If sound signal is continuously varied from `500 Hz` to `2500 Hz`, for which frequency listener will hear minimum sound intensity.
(b)
Find the frequencies in audible range `(20-20000 Hz)` for which listener will hear maximum sound intensity.

Explanation

(a) Path difference, `Delta x = S_(2)P - S_(1)P = 6.4 - 6.0 = 0.4 m`
For minimum sound intensity
`Delta x = (2n + 1) (lambda)/(2) = ((2n + 1))/(2) (v)/(f)`
`f = ((2n + 1)v)/(2 Delta x ) =((2n + 1)320)/(2(0.4))`
`= 400(2n + 1) Hz`
`n = 0,1,2....`
`n = 0, f = 400 Hz`
`n= 1, f = 1200 Hz`
`n= 2, f = 2000 Hz`
`n= 3, f = 2800 Hz`
The frequencies are `1200 Hz` and `2000 Hz.`
(b) Path difference,
`Delta x = S_(2)P - S_(1)P = sqrt((4.8)^(2) + (6.4)^(2)) - 6.4`
`= 0.8 sqrt(6^(2) + 8^(2)) - 6.4`
`= 8 - 6.4 = 1.6 m`
For maximum sound intensity
`Delta x = n lambda = (nv)/(f)`
`f = (nv)/(Delta x ) = (n xx 320)/(1.6) = 200 n`
`n = 1, f = 200 Hz`
`20000 = 200 n rArr n = 100`
`f= 200 n`, where `n - 1,2,...,100`