Two small stereo speakers A and B that are 140 m apart are s

Two small stereo speakers A and B that are 1.40 m apart are sending out sound of wavelength 33.7 cm in all directions and all in phase. A person at point P starts out equidistant from both speakers and walks (see the figure (Figure 1) ) so that he is always 1.50 m from speaker B. Limit your solutions to the cases where x?1.50m.

A) For what values of x will the sound this person hears be maximally reinforced? Enter you answers in decreasing order separating them with commas. (cm)

B) For what values of x will the sound this person hears be cancelled? Enter you answers in decreasing order separating them with commas.

Solution

a)

For Constructive Interference

|d_A-d_B|=n*lambda

where n=0,1,2,3--------

Distance from point A

n=0 =>x=1.5-0*0,337 =1.5 m =150 cm

n=1=>x-1.5-1*0.337 =1.163 m=116.3 cm

n=2=>x=1.5-2*0.337=0.826 m=82.6 cm

n=3=>x=1.5-3*0.337=0.489 m=48.9 cm

n=4=>x=1.5-4*0.337=0.152 m=15.2 cm

b)

For destructive interference

|d_A-d_B|=(n+1/2)*lambda

where n=0,1,2,3------

n=0=>x=1.5-0.5*0.337 =1.3315 m=133.15 cm

n=1=>x=1.5-1.5*0.337=0.9945 m=99.45 cm

n=2=>x=1.5-2.5*0.337=0.6575 m=65.75 cm

n=3=>x=1.5-3.5*0.337 =0.3205 m=32.05 cm