Two speakers S_1 and S_2 , powered by a common amplifier, are...

The distance between the two speakers is $d = 1.0 - (-1.0) = 2.0 \text{ m}$.

The wavelength of the sound wave is given by:
$\lambda = \dfrac{v}{f} = \dfrac{330}{600} = 0.55 \text{ m}$

For a point at a very large distance, the path difference between the sound waves reaching the man at an angle $\theta$ is $\Delta x = d \sin \theta$.

The sound intensity decreases to a minimum for the first time when the path difference is equal to $\dfrac{\lambda}{2}$.

$d \sin \theta = \dfrac{\lambda}{2}$

Substituting the values, we get:
$2.0 \sin \theta = \dfrac{0.55}{2}$

$\sin \theta = \dfrac{0.275}{2.0} = 0.1375$

For small angles, $\sin \theta \approx \theta$ (in radians), so $\theta \approx 0.1375 \text{ rad}$.

Converting to degrees:
\theta \approx 0.1375 \times \dfrac{180^{}^{{}^{\circ}}}{\pi} \approx 7.88^{}^{{}^{\circ}}

Thus, the angle is approximately 7.9^{}^{{}^{\circ}}.