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Q1: 3.14 As noted in Section 3.1, the power in a light beam is proportional to the square of its electric field, and the electric field for a beam traveling in an attenuating medium can be given by Eq. (3.8). The attenuation coefficient in that equation determines the loss. On the other hand, we more frequently discuss the loss in terms of decibels per kilometer.Show that the power change in dB/km and the attenuation coefficient a are related b yy = -8.685a, where a is given in the units km.See Answer
Q2: Below is a velocity versus time graph for an object. Use the graph to answer the questions below. A) Does the object begin at rest?How can you tell? 3) At what time does the object reverse direction?How can you tell? 1C) Determine the acceleration at the following points: t=0.5 s • t=1.2 s> t=1.4s ) Determine the displacement of the object between t = 0 and t = 1.0 seconds.See Answer
Q3: 6. In an explosion, an iron chip of 17 g mass travels at velocity of 1777 m/s. Determine the de Broglie wavelength. The speed is low enough that we can use the non-relativistic formulas.See Answer
Q4: 7. A wave propagating along the x direction according to Equation (5.18), has a maximum displacement of 4.0 cm at x = 0 and t = 0. The wave speed is 5.0 cm/s, and the wavelength is 7.0cm. (a) What is the frequency? (b) What is the wave's amplitude at x = 10 cm and t = 13 s? \Psi(x, t)=A \sin (k x-\omega t+\phi)See Answer
Q5: 1. Label (or describe) these five parts of the wave: crest, wavelength, valley, node,antinode: (5 points) See Answer
Q6: 2. If a wave strikes a surface with an angle of 25° with respect to the normal, what is the angle of reflection? (5 points)See Answer
Q7: 3. Sound travels at 1540 m/s in body tissue. If an ultrasound device sends out a frequency of 12 MHz (12,000,000 Hz) what is the wavelength of these sound waves? (10 points)See Answer
Q8:3. A closed end air column of length 3.7 m is resonating to produce a sound. a) Determine the frequency of the first harmonic if the air temperature is 24.0° C b) What frequency note would you have to play next to this air column in order to hear 5 beats per second? c) If the same air column in the same medium was resonating at the 7th harmonic, determine the new frequency.See Answer
Q9:4. Jack and Jill are going to their well to get a bucket of water. Jack drops the bucket and it falls in the well. If the well is 18.0 m deep, and it takes 1.97 seconds to hear the sound of the splash from the moment he dropped the bucket, what was the air temperature on that day?See Answer
Q10:1. Consider the oscillating system shown. Determine (a) the equation of motion of the system (b) the natural frequencies of the system x. 649 [M, M = 50 kg t M₁ K₁ = 1000 N/ X (+) 소 M = 100 kg M₂ Ik-2008 k = 2000 N/ASee Answer
Q11:1. A mass-spring damper system of M = 1 kg, K = 100 N/m is subjected to an base excitation shown. Determine: (a) The equation of motion of the system (b) The response of the system (c) The Displacement Transmissibility of the system. x(+) f [₁1 M c4 1 1 k fY(+) Y(t) = 10 Sin 74 C = 14 N₁ SSee Answer
Q12:1. A spring-mass-damper system of M -0.05 Ib.s/in, K =15 Ib/in, and C=0.7 Ib.s/in is subjected to a harmonic force F(t)=30 Cos (10t) Ibf. Determine: (a) The equation of motion of the system (b) The response as function of time (c) The value of the resonance frequency (d) The transmitted force F(+) етик X(+)See Answer
Q13:Light of 600 nm wavelength in air strikes the surface of a piece of glass (n=1.57) at 45°. Setup your coordinate system so that the interface is in the x-y plane (z=0) and the plane of incidence is x-z plane (y=0), as shown in the figure (and used in class). The electric field of the incident light is in x-z plane (a p wave) with an amplitude 25 V/m. Write the wave equations for the incident, reflected and transmitted waves.See Answer
Q14:Assignment activity and guidance Activity 1 A wing spar beam is subjected to vibrations along its length, emerging from two fuel pumps situated at opposite ends of the beam. The displacement (in mm) caused by the vibrations can be modelled by the following equations, d₁ = 2.34 sin (100nt + 570 4 d₂= 3.46 sin (100mt 3 To understand the best type, size and location of fasteners to restrain the beam (for minimum ibration), you must analyse and calculate the effect of the vibrations along its length. onsidering the above displacement equations: i) State the amplitude, phase, frequency and periodic time of each of the above equations. ii) Determine how long it takes for each machine to first produce its maximum displacement (i.e. the first instance after t = 0 ms in either the positive or negative y-direction). ii) Use the compound angle formulae to expand d₁ and dz into the form a sin(100πt) ± ß cos (100nt), where a and ß are numbers to be found. -)Using your answers from the part (iii), express d₁+ d₂ in a similar form. Analytically, convert your answer from part (iv) into the equivalent form R sin(100nt + p).See Answer
Q15:Activity 2: You are tasked with bracing the wing spar beam in activity 1 (above) with an engine pylon (second beam) secured at an angle. You have selected a cast bracket but need to check that the angle between the edges of the bracket is precisely the same angle that the beams are required to be, compared to the engineering drawing. X- O 400 mm B 250 mm 300 mm 50 mm (c) Determine the displacement vector, s = =PQ cond 101 (a) Write the position vectors along the top edge (OA) and right edge (OB) of the bracket. (b) Determine the angle (u) between the edges of the sheet-metal bracket (in the plane AOB). This whole structure is supporting the aircraft engine. In flight, a force of F = 5i +3j - 2k newton's is applied to the engine, which moves it from position P = (1, 1, 1) to position Q = (5,-1,2) (in metres). (d) Determine the work done by the force F, in moving the object from P to Q. (Work done = Force x Displacement)See Answer
Q16:Question 1 Generate a random series of 100 data points pertaining to the wave height (H) and wave period (T) for a site where the mean wave height is Hm = 2 m. The wave height should be sampled from a Rayleigh distribution with the shape parameter set to o = √2/7 and the period should be sampled from a uniform distribution between 3 and 10 s. NOTE: If you are using MS Excel to generate your data points, the following commands may be used to obtain the wave heights and periods: ● ● Wave height: =2*SQRT(2/PI())*SQRT(-2*LN(RAND())). This command is equivalent to H = Hmo√ 2 In U where U is a random number between 0 and 1. Wave period: =3+7*RAND()See Answer
Q17:Question 2 For the wave series generated in Question 1: a) What is the highest wave (Hmax and Tmax), the mean wave (Hm and Tm), and the significant wave (H, and Ts)? b) What are your Hs/Hm and Hmax/Hs ratios? How do these ratios compare to what might be expected in real data? c) Plot a histogram of the wave height H (i.e., number of waves vs. wave height), the histogram of H/Hm, and a histogram of the wave period T d) Assume we have a record of 200 waves that have H, = 6 m. What is Hmax such that there is only a 5% chance it will be exceeded?See Answer
Q18:Question 3 A hurricane has a maximum sustained local wind speed of U₁0 = 45 ms¹¹. a) What is the appropriate hurricane category? b) What is the deep-water significant wave height (,) and peak frequency (fp) of waves produced by the hurricane associated with U10? c) If this wind speed occurs over water h= 15 m deep, determine the dimensionless shallow water frequency hp and suggest whether we should use the JONSWAP or TMA spectrum to describe the waves generated by this storm. d) Plot the spectral energy density associated with this wind speed using the appropriate spectrum you identified in part (c). e) Using the spectrum from (d), determine the significant wave height H, at this depth of h = 15 m. h mg The figure above shows the cross-sectional elevation of a deployable flood barrier used to protect a community from coastal flooding. The barrier has length I and mass per unit width m (i.e., total mass per unit distance into the page) and is connected to a frictionless hinge at ground level. As flood waters rise, the barrier rotates about the hinge and adopts a position with angle such that hydrostatic equilibrium is achieved for a given inundation height h. a) Derive an expression for the water height has a function of m, 1, and 8. You may assume that the mass of the barrier is uniformly distributed. Assume a density of sea water p= 1025 kg/m³. b) Assuming m = 500 kg/m and I = 6 m, plot the water heighth as a function of 6 from 0 to 80°. c) For the assumptions stated in (b), what is the maximum level of inundation that can be accommodated by the barrier?See Answer
Q19:Generate a random series of 100 data points pertaining to the wave height (H) and wave period (T) for a site where the mean wave height is Hm = 2 m. The wave height should be sampled from a Rayleigh distribution with the shape parameter set to o = √2/ and the period should be sampled from a uniform distribution between 3 and 10 s. NOTE: If you are using MS Excel to generate your data points, the following commands may be used to obtain the wave heights and periods: ● ● Wave height: =2*SQRT(2/PI())*SQRT(-2*LN(RAND())). This command is equivalent to H = Hmo√ 2 In U where U is a random number between 0 and 1. Wave period: 3+7*RAND()See Answer
Q20:Question 2 For the wave series generated in Question 1: a) What is the highest wave (Hmax and Tmax), the mean wave (Hm and Tm), and the significant wave (H, and Ts)? b) What are your Hs/Hm and Hmax/Hs ratios? How do these ratios compare to what might be expected in real data? c) Plot a histogram of the wave height H (i.e., number of waves vs. wave height), the histogram of H/Hm, and a histogram of the wave period T d) Assume we have a record of 200 waves that have H, = 6 m. What is Hmax such that there is only a 5% chance it will be exceeded?See Answer

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