Both drawings show the same square, each of which has a side of length L = 0.90

Question

Both drawings show the same square, each of which has a side of length L = 0.90 m. An observer O is stationed at one corner of each square. Two loudspeakers are located at corners of the square, as in either drawing 1 or drawing 2. The speakers produce the same single-frequency tone in either drawing and are in phase. The speed of sound is 343 m/s. Find the single smallest frequency that will produce both constructive interference in drawing 1 and destructive interference in drawing 2.

Explanation / Answer

PART-1:- For drawing 1:
We know that for constructive interference:
|L1-L2|=n? ,L1=L2= 0.9m ,n=1
?= 0.9m
f= v/?=343/0.9= 381.1 = 381 Hz.

PART-2:- For drawing 2:
Like part 1,constructive interference:
|L1-L2|=n? ,L1=0.9*?2=1.27 m , L2=0.9m ,n=1
?= 1.27-0.9= 0.37
f= v/?=343/0.37= 927.02= 927 Hz.

destructive interference:
|L1-L2|=(n+1/2)? ,L1=0.9*?2=1.27m , L2=0.9m ,n=0
0.37=(1/2)*?
?=0.74
f= v/?=343/0.74= 463.51 = 464 Hz.

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