q2_sol - The ratio of the minimum distance along the former...

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Quiz 2 Phys. 2306 F09 CRN 94850 You may use your text book, notes, and a calculator. Two loud speakers A,B are a distance L= 2 . 00 m apart. They each emit pure tones of frequency f= 206 Hz. The speed of sound in air is 344 m/s. 1) Along the line joining the speakers and between them, the ratio of the number of con- structive interference positions to the number of destructive ones is a) < 1 b) 1 c) > 1 λ = v/f = 344 / 206 = 1 . 67 m. Thus > 1 λ , but < 1 . 5 λ can fit between the speakers. Take a point P on the line between the speakers with distance from A = AP and distance from B = BP . For constructive interference on the line connecting the speakers and between them, AP - BP = 0 , ± λ (3 places), while for destructive interference, AP - BP = ± λ/ 2 (2 places). The ratio is > 1, (c) 2) The number of constructive interference positions between speakers is a) 0 b) 1 c) 2 d) 3 e) none of these The answer is 3 (given above), (d). 3) Consider a line through speaker B that is perpendicular to the line between the speakers.
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Unformatted text preview: The ratio of the minimum distance along the former line for destructive interference to that of constructive interference is a) &amp;lt; 1 b) 1 c) &amp;gt; 1 Note PAB form a right triangle. BP,AB are the sides and AP the hypotenuse. So 1 AP &amp;gt; BP,AP = q 4 + ( BP ) 2 . For the minimum constructive interference value of BP,AP-BP = , while for destructive interference AP-BP = / 2. Thus for con-structive interference BP/AP is less than for destructive interference (just draw the right triangles). Thus the ratio you want is &amp;gt; 1, (c). Below is the full calculation. AP = q 2 . 00 2 + ( BP ) 2 . For destructive interfence the minimum BP is obtained from, q 2 . 00 2 + ( BP ) 2-BP = / 2. Thus, 2 . 00 2 + ( BP ) 2 = ( BP ) 2 + BP + 2 / 4 or BP = 4 /-/ 4 = 1 . 98 m. For constructive interference, q 2 . 00 2 + ( BP ) 2-BP = , so BP = 2 /-/ 2 = 0 . 363 m and the ratio is &amp;gt; 1, (c). 2...
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q2_sol - The ratio of the minimum distance along the former...

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