Two sound speakers are driver in phase by an audio amplifier at frequency `600 H_(Z)`. The speed of sound is `340 m//s`. The speakers are on the `y `- axis, one at `y = + 1.0 m` and the other at `y = - 1.0 m` . A listener begins at `y = 0` and walks along a line parallel to the `y` - axis at a very large distance `x` away.
(a) At what angle `theta` (between the line from the origin to the listener at the `x` - axis) will she first hear a minimum sound intensity?
(b) At what angle will she first hear a maximum (afer `theta = o^(@)`) sound intensity?
(c ) How many maxima can she possible hear if she keeps walking in the same direction?

Answer

A, B, C, D

Explanation

(a) `lambda = (nu)/(f) = (340)/(600) = 0.57 m`

`d sin theta = (lambda)/(2)`
`:. theta = sin^(-1) ((lambda)/(2d))`
`= sin^(-1) ((0.57)/(4))`
`= 8.14^(@)`
(b) `d sin theta = lambda` or `theta = sin^(-1) (lambda/(d))`
`= sin^(-1) ((0.57)/(2))`
`= 16.5^(@)`
(c ) `d sin theta = n lambda`
`:. n_(max) = (d)/(lambda)` (when `sin theta = 1`)
`= (2)/(0.57) = 3.5`
`:.` Maximum `3` maximas can be heard
corresponding to `n = 1, 2` and `3`( beyond `theta = 0^(@)`)