**Core Concept**
Pneumoperitoneum refers to the presence of free air within the peritoneal cavity, which can be a sign of a perforated viscus, trauma, or other conditions. Accurate detection of pneumoperitoneum is crucial for timely diagnosis and management.

**Why the Correct Answer is Right**
The best investigation to detect pneumoperitoneum is an upright chest X-ray (CXR). This is because free air rises to the highest point in the chest, which is the lung bases in an upright position, making it easily visible on a CXR. The air is usually seen as a thin, linear or curvilinear lucency beneath the diaphragm, often referred to as "pneumoperitoneum sign". This investigation is quick, inexpensive, and sensitive for detecting pneumoperitoneum.

**Why Each Wrong Option is Incorrect**
**Option A:** CT scan is highly sensitive for detecting pneumoperitoneum, but it is not the best initial investigation due to its higher cost and radiation exposure.
**Option B:** Abdominal X-ray can be used to detect pneumoperitoneum, but it is less sensitive than an upright CXR, especially in cases where the air is not visible in the upper abdomen.
**Option C:** Ultrasound can be used to detect pneumoperitoneum, but it is operator-dependent and may not be as sensitive as an upright CXR in detecting free air.

**Clinical Pearl / High-Yield Fact**
When performing an upright chest X-ray to detect pneumoperitoneum, it is essential to ensure the patient is standing or sitting upright, with their arms raised above their head to minimize diaphragmatic movement and improve visualization of the lung bases.

**Correct Answer:** C.