Universal jamming grippers excel at grasping unknown objects due to their compliant bodies. Traditional tactile sensors can compromise this compliance, reducing grasping performance. We present acoustic sensing as a form of morphological sensing, where the gripper's soft body itself becomes the sensor. A speaker and microphone are placed inside the gripper cavity, away from the deformable membrane, fully preserving compliance. Sound propagates through the gripper and object, encoding object properties, which are then reconstructed via machine learning. Our sensor achieves high spatial resolution in sensing object size (2.6 mm error) and orientation (0.6 deg error), remains robust to external noise levels of 80 dBA, and discriminates object materials (up to 100% accuracy) and 16 everyday objects (85.6% accuracy). We validate the sensor in a realistic tactile object sorting task, achieving 53 minutes of uninterrupted grasping and sensing, confirming the preserved grasping performance. Finally, we demonstrate that disentangled acoustic representations can be learned, improving robustness to irrelevant acoustic variations.