Volcanic tremor is a ubiquitous feature of explosive eruptions. This oscillation persists for minutes to weeks and is characterized by a remarkably narrow band of frequencies from about 0.5 Hz to 7 Hz (refs 1-4). Before major eruptions, tremor can occur in concert with increased gas flux and related ground deformation(5-7). Volcanic tremor is thus of particular value for eruption forecasting(6,8). Most models for volcanic tremor rely on specific properties of the geometry, structure and constitution of volcanic conduits as well as the gas content of the erupting magma. Because neither the initial structure nor the evolution of the magma-conduit system will be the same from one volcano to the next, it is surprising that tremor characteristics are so consistent among different volcanoes. Indeed, this universality of tremor properties remains a major enigma. Here we employ the contemporary view that silicic magma rises in the conduit as a columnar plug surrounded by a highly vesicular annulus of sheared bubbles(9,10). We demonstrate that, for most geologically relevant conditions, the magma column will oscillate or 'wag' against the restoring 'gas-spring' force of the annulus at observed tremor frequencies. In contrast to previous models, the magma-wagging oscillation is relatively insensitive to the conduit structure and geometry, which explains the narrow band of tremor frequencies observed around the world. Moreover, the model predicts that as an eruption proceeds there will be an upward drift in both the maximum frequency and the total signal frequency bandwidth, the nature of which depends on the explosivity of the eruption, as is often observed.