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Statement of a problem № 3474

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The wave function for a harmonic wave travelling in the positive x-direction with amplitude A, angular frequency w and wave number k is y1 = A sin (kx-wt). The wave interferes with another harmonic wave travelling in the same direction with the same amplitude, frequency and wave number, but with a phase difference I?. By using the principle of superposition, obtain an expression for the wave function of the resultant wave and show its amplitude is |2Acos1/2s|. If each wave has an amplitude of 6 cm and they differ in phase by pi/2, what is the amplitude of the resultant wave? For what phase differences would the resultant amplitude be equal to 6 cm? Describe the effects that would be heard if the two waves were sound waves, but with slightly different frequencies. How could you determine the differ- ence between the frequencies of the two harmonic sound sources? [you may use the result si

Solution:
The wave function for a harmonic wave travelling in the positive x-direction wit

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