Answer
a. 2.0 m.
b. Constructive.
c. 1.0m, destructive.
Work Step by Step
If the path difference between the two waves is a whole number of wavelengths, constructive interference occurs.
If it is an odd number of half-wavelengths, destructive interference occurs.
a. Let R1 be the distance from the left speaker to the observer. Let R2=8.0m be the distance from the right speaker to the observer.
a. $R1=\sqrt{(6.0m)^2+(8.0m)^2}=10.0m$. The path difference is $\Delta R = R1-R2=2.0 m$.
b. The path difference is one wavelength. Constructive interference occurs.
c. Let R2=17.0m be the distance from the right speaker to the observer. $R1=\sqrt{(6.0m)^2+(17.0m)^2}=18.0m$ The path difference is $\Delta R = R1-R2=1.0 m$.
The path difference is one-half wavelength. Destructive interference occurs.
