Answer
a. 343 Hz.
b. 1000 Hz, 1700 Hz.
Work Step by Step
a. For destructive interference, the smallest path difference is one-half wavelength. The path difference here is 0.50 m.
$$0.50m=\frac{1}{2}\lambda$$
$$\lambda = \frac{0.50m}{1/2}=1.00m$$
$$f=\frac{v}{\lambda}=\frac{343\;m/s}{1.00m}=343\;Hz$$
b. Destructive interference also occurs when the path difference is three half-wavelengths, five half-wavelengths, etc.
Find the next 2 frequencies.
$$0.50m=\frac{3}{2}\lambda$$
$$\lambda = \frac{0.50m}{3/2}=0.333m$$
$$f=\frac{v}{\lambda}=\frac{343\;m/s}{0.333m}\approx1000\;Hz$$
$$0.50m=\frac{5}{2}\lambda$$
$$\lambda = \frac{0.50m}{5/2}=0.20m$$
$$f=\frac{v}{\lambda}=\frac{343\;m/s}{0.20m}\approx1700\;Hz$$
