Given for the problem: A speaker sends out two sound waves with equal Amplitudes but the frequencies are f(1) and f(2) respectively. The motion of sound as w = A * cos(k*x - t*(Omega)). The wave number's and the angular frequency's definition are the same for light. Find for the problem: Show that at a distance x directly in front of the speaker, there is destructive interference between the waves with a frequency f(1) - f(2). My solution so far: w(1) = A * cos((2PI/(Lambda(1))) * x - (2PI * f(1) * t) w(2) = A * cos((2PI/(Lambda(2))) * x - (2PI * f(2) * t) I assume that the final equation will be in the form of: dt = (x / v) - t where v is the speed of sound A little advice please!
"Destructive Interference" in this case is time-dependent cancellation of the total amplitude (that means add the wave functions), at any location. This is in contrast to location-dependent cancellation of the total amplitude (an interference pattern) at all time. Choose an x-value, and add the wave forms ; see when (time) they cancel.