Question

Two sound speakers are driven in phase by an audio amplifier at frequency $600Hz$. The speed of sound is $340m/s$. The speakers are on the $y$-axis, one at $y=+1.0m$ and the other at $y=-1.0m$. A listener begins at $y=0$ and walks along a line parallel to the $y$-axis at a very large distance $x$ away. At what angle ${\theta }^o$ (between the line from the origin to the listener at the x-axis) will she first hear a minimum sound intensity ?

Answer 1

Geometrically the situation is similar to Young's double slit experiment, with observer walking along the screen and audio sources being on position of the slits.

Wavelength of the audio sources=$\lambda =\frac{c}{\nu }$

Path difference between sources at a point of the screen at a distance $y$ from the x-axis=$\frac{yd}{D}=dsin\theta$

For first minima, $dsin\theta =\frac{\lambda }{2}$

$⟹\sin \theta =\frac{\lambda }{2d}$

$⟹\theta =si{n}^{-1}\left(\frac{c}{2\nu d}\right)\approx 8^{\circ }$