Wavefronts and Interference

• A very brief energetic disturbance of air pressure, for example from a sparkplug, will produce a spherical wavefront that propagates away from the source (at speed $c$) uniformly in all directions. This disturbance will arrive at a distance $r$ from the source after a time delay from emission to reception of $r/c$.

• Due to the spreading of energy over an outwardly growing spherical surface area of $4 \pi r^2$, the magnitude of the pressure disturbance decreases linearly with distance from the source (sound pressure level, which is proportional to the square root of energy, will decrease by 6 dB per doubling of distance).

• Wavefronts generated by multiple sources can superpose in various ways, depending on the arrangement of the sources and the time at which the disturbances are generated. The resulting wavefront can be visualized according to Huygens' principle.

• Sound wavefronts may sometimes be primarily planar, for example when generated in cylindrical tubes or when considering a spherical wavefront very far from its source. In such cases, the magnitude of the pressure disturbance will not decrease with distance (no spherical spreading), neglecting losses.

• Wave interference results from the linear superposition of multiple wave disturbances, which can result from multiple sources and/or reflections.

• When the interacting waves contain common frequencies and fixed phase relationships, constructive and destructive interference creates steady spatial patterns of high and low amplitude (resulting in standing wave patterns on a fixed string or acoustic resonances in a room).