Question

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Explanation:

Step1: Calculate wavelength of sound

First, use the wave speed formula $v = f\lambda$ to solve for wavelength $\lambda$. Rearrange to $\lambda = \frac{v}{f}$.
$\lambda = \frac{360\ \text{m/s}}{30\ \text{Hz}} = 12\ \text{m}$

Step2: Find path difference

Calculate the difference in distance from the two speakers to the listener.
$\Delta d = 96\ \text{m} - 60\ \text{m} = 36\ \text{m}$

Step3: Compare path difference to wavelength

Determine how many wavelengths fit into the path difference.
$\frac{\Delta d}{\lambda} = \frac{36\ \text{m}}{12\ \text{m}} = 3$
This is an integer multiple, so the waves are in phase.

Step4: Match to diagram and interference type

In-phase waves align peaks/troughs, matching Diagram I. Integer multiple path difference causes constructive interference.

Answer:

Diagram I, constructive (Row 1: Diagram I, constructive)