**Core Concept**
The structure being described is a type of airway in the lung, characterized by the presence of smooth muscle and cartilage in its wall. This is a key feature that distinguishes it from other types of airways.

**Why the Correct Answer is Right**
The tubule described is a bronchiole, which is a smaller airway that branches off from the larger bronchi. The presence of smooth muscle in the wall of the bronchiole allows for bronchoconstriction, which is an important mechanism for regulating airflow in the lungs. The cartilage in the wall of the bronchiole provides additional support and helps to maintain the patency of the airway.

**Why Each Wrong Option is Incorrect**
**Option A:** This is incorrect because a bronchus is a larger airway that does not have the same level of smooth muscle and cartilage as a bronchiole.
**Option B:** This is incorrect because a bronchiolar duct is not a standard anatomical term and does not accurately describe the structure being asked about.
**Option C:** This is incorrect because an alveolar duct is a small airway that connects the respiratory bronchioles to the alveoli, but it does not have the same level of smooth muscle and cartilage as a bronchiole.

**Clinical Pearl / High-Yield Fact**
It's worth noting that the airways in the lungs can be broadly categorized into three types: bronchi, bronchioles, and alveoli. The bronchi are the largest airways and are found in the larger airways, while the bronchioles are smaller and are found in the smaller airways. The alveoli are the smallest airways and are found at the end of the respiratory tree.

**Correct Answer:** C.