Two speakers `S_(1) and S_(2)` derived by the same amplifier and placed at `y = 1.0 m and y = - 1.0 m` (Fig . 7.9) The speakers vibrate in phase at `600 Hz`. A man stands at a point on the x - axis at a very large distance from the origin and starts moving parallel to the Y - axis . The speed of sound in air is `330 m//s`.
(a). At what angle will the intensity of sound drop to a minimum for the first time ?
(b) At what angle will the sound intensity be maximum for the first time ?
(c ) If he continues to walk along the line , how many more maxima can he hear ?

Explanation

When the man is at a large distance from the speaker , the path differnces between waves starting from `S_(1) and S_(2)` and reachind at `Q ` will be ` Delta = S_(2) Q - S_(1) Q = S_(1) S_(2) sin theta = 2 sin theta ~~ 2 tan theta = theta`
Also ` lambda = (v)/( n) = ( 330)/( 600) = 0.55 m`
(a) For the first minima
Path differnce ` Delta = ( lambda)/( 2)`
` 2 theta = ( 0.55) /( 2)`
` theta = ( 0.55)/( 4) = 0.1375 rad = 79^(@)`
(b) For the first maxima , `Delta = lambda rArr 2 theta = 0.55`
` theta = ( 0.55)/(2) rad = 15.8^(@)`
(c ) Maximum path difference ` = 2 m`
If order of maxima is ` r , then 2 = r lambda`
`r = (2)/( lambda) = (2)/( 0.55) = 3.6 ~~ 3`
Number of more maxima ` = 3 - 1 = 2`