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oldhw39 - oldhomework 39 Turner(58185 This print-out should...

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This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Two similar tuning forks produce sound waves of the same 2 . 9 mPa amplitude. One tuning fork y 1 has a frequency 936 s 1 and the other y 2 has a frequency of 1040 s 1 . These two tuning forks produce interference. + A + A - A -A 0 0 T beat T wave y 1 y 2 y 1 + y 2 + A - A 0 0 3 T beat 6 T beat What is the number of beats per second that is heard? Correct answer: 104 Hz. Explanation: Let : A = 2 . 9 mPa , f 1 = 936 s 1 , and f 2 = 1040 s 1 . +5 . 5 - 5 . 5 A (mPa) t (milli-seconds) 9 . 6 ms 19 . 2 ms y 1 y 2 y 1 + y 2 +5 . 5 - 5 . 5 A (mPa) t (milli-seconds) 28 . 8 ms 57 . 6 ms Two harmonic waves are described by y 1 = A cos( k x - ω 1 t ) and y 2 = A cos( k x - ω 2 t ) . f 2 - f 1 2 = 52 s 1 , f 1 + f 2 2 = 988 s 1 , T wave = 1 f 2 - f 1 2 = 19 . 2 ms , ω 1 = 2 π f 1 = 2 π (936 s 1 ) = 5881 . 06 rad / s , ω 2 = 2 π f 2 = 2 π (1040 s 1 ) = 6534 . 51 rad / s , ω 2 - ω 1 2 = 326 . 726 rad / s , ω 2 + ω 1 2 = 6207 . 79 rad / s , oldhomework 39 – Turner – (58185) 1

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hinojosa (jlh3938) – oldhomework 39 – Turner – (58185) 2 and y 1 + y 2 = 2 A cos bracketleftbigg parenleftbigg ω 1 - ω 2 2 parenrightbigg t bracketrightbigg × cos bracketleftbigg parenleftbigg ω 1 + ω 2 2 parenrightbigg t bracketrightbigg A = 2 A cos bracketleftbigg parenleftbigg ω 1 - ω 2 2 parenrightbigg t bracketrightbiggvextendsingle vextendsingle vextendsingle vextendsingle max = 2 (2 . 9 mPa) · cos bracketleftbigg ( - 326 . 726 rad / s) t bracketrightbiggvextendsingle vextendsingle vextendsingle vextendsingle max = 5 . 8 mPa , where A is the amplitude of the sum of the two waves y 1 + y 2 , and A is the amplitude of either wave y 1 or y 2 . The wave produced by the interference of two waves of frequencies f 2 and f 1 , respec- tively, has frequency f wave f 2 - f 1 2 , where f 2 > f 1 = 1040 s 1 - 936 s 1 2 = 52 s 1 , and the period T wave 1 f wave = 1 52 s 1 = 19 . 2 ms . Since we hear two beats per cycle of the re- sultant wave ( T wave = 2 T beat ), the beat fre- quency is f beat = 2 f wave = 2 (52 s 1 ) = 104 s 1 , twice the frequency of the wave.
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oldhw39 - oldhomework 39 Turner(58185 This print-out should...

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