The two speakers of a boom box are 35.0 cm apart. A single oscillator makes the speakers vibrate in phase at frequency of 2.00 kHz. At what angles, measured from the perpendicular bisector of the line joining the speakers, would a distant observer hear maximum sound intensity? Minimum sound intensity? (Take the speed of sound as 340 m/s.)

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Filo · Accepted Answer

λ=2.000Hz340m/s​=0.170mThe maxima are located at dsinθ=mλ:m=0 gives           θ=0∘m=1 gives            	heta = sin^\left ( {-1} \dfrac{\lambda}{d} ight ) = sin^{-1}\left ( \dfrac{0.170 m}{0.350 m} ight ) = 29.1^{\circ} m=2 gives           θ=sin−1(d2λ​)=sin−1[0.350m0.170m​]=76.3∘m=3 has no solution, since sinθ>1.The minima are located at dsinθ=(m+21​)λ:m=0 gives           θ=sin−1( 2dλ​) =sin−1[ 2(0.350m)0.170m​] =14.1∘m=1 gives           θ=sin−1( 2d3λ​) =sin−1[ 2(0.350m)3(0.170m)​] =46.8∘m=2 has no solution, since sinθ>1.We have maxima at 0∘,29.1∘, and 76.3∘; minima at 14.1∘ and 46.8∘

Question Text	The two speakers of a boom box are 35.0 cm apart. A single oscillator makes the speakers vibrate in phase at frequency of 2.00 kHz. At what angles, measured from the perpendicular bisector of the line joining the speakers, would a distant observer hear maximum sound intensity? Minimum sound intensity? (Take the speed of sound as 340 m/s.)
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