Two speakers connected to the same source of fixed frequency are placed $2\text{ m}$ apart in a box. A…
Two speakers connected to the same source of fixed frequency are placed $2\text{ m}$ apart in a box. A sensitive microphone placed at a distance of $4\text{ m}$ from the mid-point along the perpendicular bisector shows maximum response. The box is slowly rotated till the speakers are in line with the microphone. The distance between the mid-point of the speakers and the microphone remains unchanged. Exactly 5 maximum responses (including the initial and last one) are observed in the microphone in doing this. The wavelength of the sound wave is
(a) $0.8\text{ m}$
(b) $0.5\text{ m}$
(c) $0.2\text{ m}$
(d) $1.6\text{ m}$
Solution
In the starting, $\Delta x = 0$ and maximum intensity is observed.
Next maxima will correspond to $\Delta x = \lambda$, i.e. 5th maxima will correspond to
The diagram shows two speakers $S_1$ and $S_2$ separated by 2 m with midpoint $O$, and microphone $D$ located 4 m from $O$, reorienting relative to $D$.
$\Delta x = 4\lambda$. But $\Delta x = S_1S_2 = 2\text{ m}$
$\therefore 4\lambda = 2$ or $\lambda = 0.5\text{ m}$
[Here $S_1$ and $S_2$ are two speakers placed 2 m apart and $D$ is microphone at 4 m from point $O$ (mid-point of $S_1S_2$)]