# hw13 - irshad(si2865 – HW13 – distler –(57205 1 This...

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Unformatted text preview: irshad (si2865) – HW13 – distler – (57205) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. In the question which asks ”What is the power transmitted by the wave?”, what is requested is the RMS power, which is 1/2 of the peak power, since cos 2 averagesto 1 / 2 , overacompletecycle. 001 10.0 points Two harmonic waves traveling in opposite di- rections interfere to produce a standing wave described by y = 3 sin( k x ) cos(5 t ) where k = 3 . 8 m − 1 , x is in meters and t is in seconds. What is the wavelength of the interfering waves? Correct answer: 1 . 65347 m. Explanation: Let : k = 3 . 8 m − 1 . For a standing wave described by y = A sin( k x ) cos( ω t ) , its wavelength is λ = 2 π k = 2 π 3 . 8 m − 1 = 1 . 65347 m . keywords: 002 10.0 points A wave pulse on a string is described by the equation y 1 = A ( B x- C t ) 2 + D and a second wave pulse on the same string is described by y 2 =- A ( B x + C t- E ) 2 + D , where x is in meters and t in seconds, and A = 9 . 17 m, B = 3 . 48 m − 1 , C = 5 . 25 s − 1 , D = 2 . 29, and E = 7 . 99. At what time will the two waves exactly cancel everywhere? Correct answer: 0 . 760952 s. Explanation: Let : A = 9 . 17 m , B = 3 . 48 m − 1 , C = 5 . 25 s − 1 , D = 2 . 29 , and E = 7 . 99 . According to superposition principle y = y 1 ( x, t ) + y 2 ( x, t ) . Since y = y 1 + y 2 , y will be zero when y 1 =- y 2 A ( B x- C t ) 2 + D =- A ( B x + C t- E ) 2 + D B x- C t = ± ( B x + C t- E ) (3 . 48 m − 1 ) x- (5 . 25 s − 1 ) t = ± [(3 . 48 m − 1 ) x +(5 . 25 s − 1 ) t- 7 . 99] . (The ± arises from taking a square root.) Using the “+” sign, 2 C t = E t = E 2 C = 7 . 99 2 (5 . 25 s − 1 ) = . 760952 s . Because x cancels out, our solution tells us y is zero for all positions x at this particular time t . 003 10.0 points A right-moving transverse wave on a string has the form of a pulse shown. v irshad (si2865) – HW13 – distler – (57205) 2 The energy density in the wave, plotted at this same instant in time, is 1. 2. 3. 4. 5. correct 6. 7. 8. 9. Explanation: E ∝ parenleftbigg ∂y ∂x parenrightbigg 2 , so the energy density will have the following shape. 004 (part 1 of 4) 10.0 points A sinusoidal wave on a string is described by the equation y = A sin( k x- ω t ) , where A = 0 . 11 m, k = 0 . 69 m − 1 , and ω = 36 rad / s. If the mass per unit length of this string is 12 g / m, what is the speed of the wave?...
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hw13 - irshad(si2865 – HW13 – distler –(57205 1 This...

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