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Old Homework 39

# Old Homework 39 - portillo(gdp347 – oldhomework 39 –...

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Unformatted text preview: portillo (gdp347) – oldhomework 39 – Turner – (58185) 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 2 . 9 mPa amplitude. One tuning fork y 1 has a frequency 1044 s − 1 and the other y 2 has a frequency of 1160 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: 116 Hz. Explanation: Let : A = 2 . 9 mPa , f 1 = 1044 s − 1 , and f 2 = 1160 s − 1 . +5 . 5- 5 . 5 A (mPa) t (milli-seconds) 8 . 6 ms 17 . 2 ms y 1 y 2 y 1 + y 2 +5 . 5- 5 . 5 A (mPa) t (milli-seconds) 25 . 8 ms 51 . 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 = 58 s − 1 , f 1 + f 2 2 = 1102 s − 1 , T wave = 1 f 2- f 1 2 = 17 . 2 ms , ω 1 = 2 π f 1 = 2 π (1044 s − 1 ) = 6559 . 65 rad / s , ω 2 = 2 π f 2 = 2 π (1160 s − 1 ) = 7288 . 49 rad / s , ω 2- ω 1 2 = 364 . 425 rad / s , ω 2 + ω 1 2 = 6924 . 07 rad / s , portillo (gdp347) – oldhomework 39 – Turner – (58185) 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 (2 . 9 mPa) · cos bracketleftbigg (- 364 . 425 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 = 1160 s − 1- 1044 s − 1 2 = 58 s − 1 , and the period T wave ≡ 1 f wave = 1 58 s − 1 = 17 . 2 ms ....
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Old Homework 39 - portillo(gdp347 – oldhomework 39 –...

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