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Two students in a dorm room listen to a pure tone produced by two loudspeakers that are in phase. Students A and B in...

Two students in a dorm room listen to a pure tone produced by two loudspeakers that are in phase. Students A and B in the figure(Figure 1) hear a maximum sound. What is the lowest possible frequency of the loudspeakers?


I know the answer is .18KHz because it is in the back of the book, however I really want to understand how to get the answer so could you please show as much detailed math as possible to get to the answer? I will rate high!! Thanks so much!

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Answer #2

Student A always hear maximum independent of the frequency.

for student B:

path difference = d = sqrt(3*3+1.5*1.5) - 1.5 = 1.8541 m

wavelength for hearing a maximum sound must be equal to the path difference:

lamda = d = 1.8541 m

frequancy = v/lamda = 343/ 1.8541 = 184.995 = 0.18 kHz


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