Given:

the wavelength of the sound will be

\(\displaystyle\lambda={\frac{{{v}}}{{{f}}}}\)

\(\displaystyle={\frac{{{345}\frac{{m}}{{s}}}}{{{690}{H}{z}}}}\)

a) for the first relative maximum we get

\(\displaystyle{d}_{{1}}={d}_{{2}}+\lambda\)

from the figure using the pythagorous theorem we get

\(\displaystyle{\left({d}_{{2}}+\lambda\right)}^{{2}}={{d}_{{2}}^{{2}}}+{\left({0.820}{m}\right)}^{{2}}\)

\(\displaystyle{d}_{{2}}=\ldots\)

b) for the first relative minimum we get

\(\displaystyle{d}_{{1}}={d}_{{2}}+{\left(\frac{\lambda}{{2}}\right)}\)

from the figure using the pythagoroustheorem we get

\(\displaystyle{\left({d}_{{2}}+{\left(\frac{\lambda}{{2}}\right)}\right)}^{{2}}={{d}_{{2}}^{{2}}}+{\left({0.820}{m}\right)}^{{2}}\)

\(\displaystyle{d}_{{2}}=\ldots\)