old34 - hernandez(ejh742 – oldhomework 34 – Turner...

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Unformatted text preview: hernandez (ejh742) – oldhomework 34 – Turner – (58120) 1 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 6 . 2 mPa amplitude. One tuning fork y 1 has a frequency 624 s − 1 and the other y 2 has a frequency of 728 s − 1 . These two tuning forks produce interference. + A + A- A-A T beat T wave y 1 y 2 y 1 + y 2 + A- A 3 T beat 6 T beat What is the number of beats per second that is heard? Correct answer: 104 Hz. Explanation: Let : A = 6 . 2 mPa , f 1 = 624 s − 1 , and f 2 = 728 s − 1 . +12- 12 A (mPa) t (milli-seconds) 9 . 6 ms 19 . 2 ms y 1 y 2 y 1 + y 2 +12- 12 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 = 676 s − 1 , T wave = 1 f 2- f 1 2 = 19 . 2 ms , ω 1 = 2 π f 1 = 2 π (624 s − 1 ) = 3920 . 71 rad / s , ω 2 = 2 π f 2 = 2 π (728 s − 1 ) = 4574 . 16 rad / s , ω 2- ω 1 2 = 326 . 726 rad / s , ω 2 + ω 1 2 = 4247 . 43 rad / s , hernandez (ejh742) – oldhomework 34 – Turner – (58120) 2 and y 1 + y 2 = 2 A cos bracketleftbiggparenleftbigg ω 1- ω 2 2 parenrightbigg t bracketrightbigg × cos bracketleftbiggparenleftbigg ω 1 + ω 2 2 parenrightbigg t bracketrightbigg A = 2 A cos bracketleftbiggparenleftbigg ω 1- ω 2 2 parenrightbigg t bracketrightbiggvextendsingle vextendsingle vextendsingle vextendsingle max = 2 (6 . 2 mPa) · cos bracketleftbigg (- 326 . 726 rad / s) t bracketrightbiggvextendsingle vextendsingle vextendsingle vextendsingle max = 12 . 4 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 = 728 s − 1- 624 s − 1 2 = 52 s − 1 , and the period T wave ≡ 1 f wave = 1 52 s − 1 = 19 . 2 ms ....
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old34 - hernandez(ejh742 – oldhomework 34 – Turner...

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