a person stands 3.00 m from one speaker and 4.00 m from an identical speaker. if there is a destructive…

Explanation:

Step1: Calculate path - difference

The path - difference $\Delta r$ between the two waves is the difference in the distances from the two speakers to the person. $\Delta r=4.00 - 3.00=1.00$ m.

Step2: Use destructive - interference condition

For destructive interference, the condition is $\Delta r=(n+\frac{1}{2})\lambda$, where $n = 1$. Substituting $n = 1$ into the formula, we get $\Delta r=(1+\frac{1}{2})\lambda=\frac{3}{2}\lambda$.

Step3: Solve for wavelength

Since $\Delta r = 1.00$ m and $\Delta r=\frac{3}{2}\lambda$, we can solve for $\lambda$. Rearranging the equation $\lambda=\frac{2\Delta r}{3}$. Substituting $\Delta r = 1.00$ m, we have $\lambda=\frac{2\times1}{3}=\frac{2}{3}\approx0.67$ m.

Answer:

$\frac{2}{3}$ m