phyics 53 lecture dr. brown 7 december 2010 recall superposition principle applies to wave equation for waves on string, sound, electromagnetic consider two sources with slightly different wave numbers and wave frequencies find sum using trig sub and then note that Intensity is proportional to amplitude squared beats = one interesting result of superposition [slowly varying intensity with beat frequency = f_2-f_1 standing waves resonance modes for: string fixed at both ends fixed at one end and free at the other organ pipe closed at one end and open at the other determination for speed of sound in gas