Two small stereo speakers A and B that are 1.40 m apart are sending out sound of

Question

Two small stereo speakers A and B that are 1.40 m apart are sending out sound of wavelength 34.1 cm in all directions and all in phase. A person at point P starts out equidistant from both speakers and walks (see (Figure 1) ) so that he is always 1.50 m from speaker B . Limit your solutions to the cases where x1.50m .

A)

For what values of x will the sound this person hears be maximally reinforced?

Express your answers in decreasing order to three significant figures, separated by commas.

B)

For what values of x will the sound this person hears be cancelled?

Express your answers in decreasing order to three significant figures, separated by commas.

Explanation / Answer

=0.341 m
assume Constructive interference
|L1-L2|=n , (n=0,1,2,3..)
Distance from point A (xm)
P1: n=0 , d=1.5-0*0.341= 1.5 m
P2: n=1 , d=1.5-1*0.341= 1.159 m
P3: n=2 , d=1.5-2*0.341= 0.818m
P4: n=3 , d=1.5-3*0.341= 0.477 m
P5: n=4 , d=1.5-4*0.341= 0.136m

assume Destructive interference
|l1-l2|=(n+1/2) , (n=0,1,2,3..)
Distance from point A (xm)
P1: n=0 , d=1.5-0.5*0.341= 1.3295 m
P2: n=1 , d=1.5-1.5*0.341= 0.9885 m
P3: n=2 , d=1.5-2.5*0.341= 0.6475 m
P4: n=3 , d=1.5-3.5*0.341= 0.3065 m

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