91Ó°ÊÓ

Distance between speakers: $12\mathrm{m}$

Frequency emitted: $688\text{ H³ú}$

For constructive interference the path difference is an integeral multiple of wavelengths and for destructive interference the path difference is a half-integeral multiple of wavelengths.

The wavelength is,

$v=\mathrm{λ}f$

where v is the wave velocity, f is the frequency and$\mathrm{λ}$is the wavelength of the wave.

role="math" localid="1655809355177"

To shift from point of constructive interference to the point of destructive interference, the path difference must change by $\mathrm{λ}/2$. If you move a distance x toward speaker B, the distance to B gets shorter by $x$ and the distance to A gets longer by $x$so the path difference changes by $2x$.

$\begin{array}{c}2x=\frac{\mathrm{λ}}{2}\\ x=\frac{\mathrm{λ}}{4}\\ =\frac{0.5\text{″¾}}{4}\\ =0.125\text{″¾}\end{array}$

Hence, you must walk$0.125\mathrm{m}$ toward speaker B to move to a point of destructive interference.