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Two sound waves are produced with similar frequencies. The equations describing the pressure waves are: P1(x,t)=Posin(k1x1t) P2(x,t)=Posin(k2x2t) Using the trig identity sin()+sin()=2sin(12(+))cos(12()) , it can
Two sound waves are produced with similar frequencies. The equations describing the pressure waves are: P1(x,t)=Posin(k1x1t) P2(x,t)=Posin(k2x2t) Using the trig identity sin()+sin()=2sin(12(+))cos(12()) , it can be shown that the combined pressure at time t is Pc(x,0)=2sin(k1+k22x1+22t)cos(k1k22x122t) The beat envelope oscillates at frequency fbeat=|f1f2| , and so the cosine factor with the 12 is the beat envelope factor. One wave has frequency f=324Hz and the other has frequency f=325.36Hz . The speed of the waves is v=343m/s . The combined pressure is zero at x=0m and t=0s ; what is the next value of x>0 in which the pressure is zero at t=0s
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