Answer
a. Constructive.
b. 0.34 m.
c. 0.68 m.
Work Step by Step
The sound will be maximally reinforced when the path difference is an integer multiple of wavelengths.
The sound will be canceled when the path difference is an odd multiple of half wavelengths.
Find the wavelength.
$$\lambda=\frac{v}{f}=\frac{340.0 m/s}{250.0 Hz}=1.36 m$$
a. The path difference is zero. The interference is constructive.
b. We are told that destructive interference occurs. When she walks a distance d toward one speaker, $r_2$ increases by d and $r_1$ decreases by d, so the path difference changes by 2d.
The path difference equals half a wavelength.
$$2d=\frac{\lambda}{2}$$
$$d=\frac{\lambda}{4}=\frac{1.36m}{4}=0.34 m$$
c. Now, constructive interference occurs. The path difference equals a wavelength.
$$2d=\lambda $$
$$d=\frac{\lambda}{2}=\frac{1.36m}{2}=0.68 m$$
