Final answer:
An axial mode occurs when a standing wave is formed along the length of an object, while a tangential mode occurs when a standing wave is formed around the circumference of an object.
Step-by-step explanation:
An axial mode occurs when a standing wave is formed along the length of an object, such as a string, tube, or rod. This happens when the frequency of the driving force matches the natural frequency of the object. The nodes and antinodes of the standing wave are aligned along the length of the object, creating regions of high and low amplitude.
In contrast, a tangential mode occurs when a standing wave is formed around the circumference of an object. This typically happens when the object has a circular or cylindrical shape. The nodes and antinodes of the tangential mode are arranged in a pattern around the object, creating regions of high and low amplitude.
The occurrence of an axial mode or a tangential mode depends on the shape and dimensions of the object, as well as the driving frequency. An axial mode is more likely to happen in elongated objects, like a string or a tube, while a tangential mode is more likely to happen in objects with a circular or cylindrical shape, like a drum or a pipe.