Answer
$\theta = \pm 16.0^{\circ}, \pm 33.4^{\circ}, \pm 55.6^{\circ}$.
Work Step by Step
The silent points are located at angles that satisfy
$sin \theta=\frac{m \lambda}{a}$, where $m=\pm 1, \pm 2…$.
The wavelength $\lambda=\frac{v}{f}=\frac{344m/s}{1250Hz}=0.2752 m$.
Find the first angle.
$$sin \theta_1=\frac{\lambda}{a}$$
$$\theta_1 = sin^{-1}(\frac{0.2752 m }{1.00m})=16.0^{\circ}$$
Find the second angle.
$$sin \theta_2=\frac{2 \lambda}{a}$$
$$\theta_2 = sin^{-1}(2 \frac{0.2752 m }{1.00m})=33.4^{\circ}$$
Find the third angle.
$$sin \theta_3=\frac{3 \lambda}{a}$$
$$\theta_3 = sin^{-1}(3 \frac{0.2752 m }{1.00m})=55.6^{\circ}$$
Someone at these angles, on either side of the centerline, will hear no sound.
There are no other real solutions for m = 4, 5, etc.
