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Q1: COURSEWORK BRIEFING SHEET COURSE MODULE (and code): ASSIGNMENT TITLE: Coastal and Estuary Processes (CIVE487) Wave Theory Aims: The exercise is designed to allow students to (1) use linear wave theory for the solution of a series of simple problems of practical importance and to consider its limits of applicability and (2) carry out time domain analysis for the short-term random wave record. Details: 1. Use linear wave theory to complete the following table: Wave height, Water depth, Wave- length, H (m) d (m) L (m) Wave period, T (s) Wave celerity, C (m/s) (i) 3 5+i 40 (ii) 2 10+i 7 (iii) 1 15+i 8 i is the last digit of your student ID 2. What parameters are used to establish whether waves may be satisfactorily described by linear wave theory? [30 marks] [10 marks] 3. Classify the wave conditions in question 1 as either linear or non-linear and indicate, for the non-linear condition(s), an analytical theory (or theories) suitable for describing the waves. [10 marks] 4. For the case(s) for which linear wave theory is identified as unsuitable in question 3, note what effects the non-linearity would have on the calculated values in question 1. [10 marks] 5. Estimate the wave group velocity in a water depth of 30m if the wave period is 9s. [10 marks] 6. Estimate the wave power per unit length of wave crest in a train of regular waves if the wave height is 2m, the wavelength is 50m and the water depth is 15m. [10 marks] 7. A wave record taken during a storm is analysed by zero up crossing and contains 205 waves. The average wave height is 1.72m. Using Rayleigh distribution to i) estimate Hs, Hrms and H₁/10- ii) determine the number of wave in the record that would exceed 2.0+i/10 (i is the last digit of your student ID) [20 marks] d/Lo C d/L kd tanh kd sinh kd cosh kd n = 7007 K S 0.0000 0.0010 0.0126 0.079 0.0011 0.0132 0.083 0.0012 0.0138 0,087 0.0013 0.0144 0.091 0,0014 0.0149 0,094 0.0000 0.000 0.000 0.079 0.079 1.003 0.083 0.083 1.003 0,087 0.087 1,004 0.000 1.000 1.000 0.998 2.515 0.998 2.457 0.997 2.404 : 0.090 0,091 1.004 0.997 2.357 0.094 0.094 1.004 0.997 2,314 0.0015 0.0155 0.0016 0.0160 0.100 0.0017 0.0165 0.0018 0.0170 0.0019 0.0174 0.097 0.097 0,097 1,005 0.997 2,275 0.100 0.101 1.005 0.997 2,239 0.104 0.103 0.104 1,005 0.996 2,205 0.107 0.106 0.107 1.006 0.996 2,174 0.109 0.109 0.110 1.006 0.996 2,146 0.0020 0.0179 0.0022 0.112 0.112 0.113 1,006 0.996 2,119 0.0188 0.118 0.117 0.118 1.007 0,0024 0.995 2.069 0.0196 0,123 0,122 0.123 0.0026 1.008 0.995 2.025 0,0204 0,128 0.127 0.129 1.008 0.995 1.986 0.0028 0.0212 0.133 0.132 0.133 1.009 0.994 1,950 0,0030 0,0219 0.138 0.137 0.138 1.009 0,0032 0,994 1.917 0,0226 0.142 0.141 0.143 1,010 0,0034 0,0233 0,0036 0.993 1,887 0.147 0,146 0.147 1.011 0,993 1.859 0,0240 0.151 0.150 0.0038 0.152 1.011 0.992 1.834 0.0247 0.155 0.154 0.156 1,012 0.992 1.810 0,0040 0.0253 0.159 0.158 0,160 1,013 0.992 0.0042 0.0044 0.0266 0.167 0.0046 0,0272 0.171 0.0048 0,0278 1.787 0.0260 0.163 0.162 0,164 1,013 0.991 1,766 0.166 0,168 1.014 0.991 1.746 0.169 0.172 1.015 0.990 1.727 0.175 0.173 0,175 1.015 0.990 1,710 0,0050 0.0284 0,0055 0.178 0,176 0.179 1.016 0.990 1,693 0.0298 0,187 0.185 0.188 0,203 0,0095 0.0060 0.0311 0.195 0.0065 0.0324 0.0070 0,0336 0.0075 0,0348 0.221 1.024 0.0080 0.0360 0.226 0.222 0.228 1,026 0,0085 0,0371 0,233 0.229 0.235 1.027 0.0090 0.0382 0.240 0,236 0,242 0.0393 0.247 0.242 0.249 0.193 0.197 0,201 0.205 1.018 0,989 1.019 0.987 1.021 1.654 1,620 0,986 1,589 0,211 0.208 0,213 1.022 0,985 1,561 0,219 0,215 0.984 1,536 0.983 1.512 0.982 1.491 1,029 0.981 1.471 1.031 0.980 1.452 Linear wave theory, table of functions C d/Lo d/L kd tanh kd sinh kd cosh kd n = KS 5 0.0100 0.0403 0.253 0.248 0.256 1.032 0.979 1,435 0.0110 0,0120 0.0423 0,266 0.260 0.0443 0.278 0,269 1.036 0,271 0.282 0,0130 0.0140 0,0461 0.290 0.0479 0,282 0,294 0,977 1.403 1,039 0,975 1,375 1,042 0.973 1.350 0.301 0,292 0.306 1.046 0.971 1,327 0.0150 0.0496 0,0160 0,0513 0.322 0.0170 0,0530 0.333 0.321 0.0180 0.0546 0,312 0,302 0.317 1.049 0.969 1.307 0,312 0.328 1.052 0.967 1.288 0.339 1.056 0.965 1,271 0.343 0.330 0.350 1.059 0,963 1.255 0.0190 0,0561 0.353 0,339 0.360 1.063 0.961 1.240 0,0200 0.0576 0,362 0,347 0.370 1.066 0.959 0,0220 0.0606 1.226 0.381 0,363 0.390 1.073 0.955 0.0240 0.0634 1.201 0.398 0,379 0.409 1.080 0.951 0.0260 1.179 0.0661 0,416 0,393 0.428 1.088 0.947 0.0280 0.0688 1,159 0.432 0.407 0.446 1.095 0.943 1.141 0.0300 0.0713 0.448 0,420 0.463 1,102 0,939 1.125 0.0320 0,0738 0.464 0.0340 0,0763 0.479 0,0360 0.0787 0,0380 0,0810 0.433 0.481 1.110 0.935 1.111 0.446 0.509 0,494 0.458 0.469 0.498 0.515 1.125 0.531 1.132 1.117 0.931 1.098 0,927 1.086 0.923 1.075 0,0400 0.0833 0.0440 0.0420 0.0855 0,537 0,491 0.523 0.480 0.548 1.140 0.919 1.064 0.564 1.148 0.915 1.055 0.0877 0,551 0,501 0.580 1,156 0.911 1,046 0,0460 0,0480 0.0920 0.578 0.0899 0.565 0.512 0,595 1.164 0.908 1,038 0,521 0,611 1.172 0.904 1.030 0,0500 0.0942 0,592 0.531 0,627 1.180 0.900 0,0550 1,023 0,0993 0,624 0.554 0.665 1.201 0.890 1.007 0,0600 0,1043 0.655 0.0650 0.1092 0.686 0.0700 0,1139 0,716 0,575 0.703 1.223 0.881 0.993 0,595 0.741 1,245 0.872 0.981 0,614 0,779 1.267 0.863 0.971 0,0750 0.1186 0,745 0.632 0.816 0.0800 0.1232 0,774 0.649 0,0850 0,1277 0,803 0.665 0.0900 0,1322 0.831 0,681 0.0950 0.1366 0,858 0.695 1,291 0.854 0.962 0,854 1,315 0.845 0.955 0.892 1.340 0.836 0,948 0.929 1,365 0.827 0.968 1.392 0.942 0.819 0.937 Linear wave theory, table of functions (continued) C d/Lo d/L kd tanh kd sinh kd cosh kd n = 0.1000 0.1100 0,1410 0,886 0.1496 0,1200 0.1581 0,994 0.1300 0,1666 0.1400 0.1750 0.709 1,006 1,419 0.810 0.933 0.940 0.735 1.085 1.475 0.794 0.926 0,759 1,165 1,536 0.778 0.920 1.047 0.780 1,248 1.600 0.762 0.917 1.099 0,800 1,334 1.668 0,747 0.915 0.1500 0.1833 1.152 0,818 1.424 1.740 0,732 0.913 0.1600 0.1916 1.204 0.835 1,517 1.817 0,718 0.913 0.1700 0,2000 1.256 0.850 1.614 1,899 0.705 0.913 0,1800 0.2083 0.1900 0.2167 1.362 0.2000 0.2200 0.2421 1,309 0,864 1,716 1.986 0.692 0.914 0.877 1.823 2,079 0.680 0.916 0.2251 1,414 0.888 1.521 0.909 0,2400 0.2592 1,629 0.926 1.936 2,179 2,397 2.451 2.179 0.668 0.918 0.2600 0,2766 1.738 0.940 2.755 2,647 2,931 0.2800 0,2942 1.849 0.952 3,097 3.255 0,646 0,923 0.626 0.608 0.936 0.592 0.942 0.929 0.3000 0,3121 1.961 0,961 3,483 3.624 0.578 0.949 0,3200 0,3400 0.3486 2.190 0.3303 2,075 0,969 3,920 4,045 0,565 0,955 0,975 4,414 4.525 0.555 0.961 0.3600 0.3672 2.307 0.3800 0.3860 2,425 0.980 4,973 5.073 0.546 0.967 0.984 5,608 5,697 0.538 0.972 0,4000 0.4050 0.4200 0,4241 2,665 0.4400 0,4434 2.786 0.4600 0.4628 2,544 0.988 6,329 6,407 0.531 0.976 0.990 7.147 7.216 0.526 0.980 0.992 8.075 8.137 0.521 0.983 2,908 0.994 9.129 9.183 0,517 0.986 0,4800 0.4822 3.030 0,995 10,32 10,37 0.514 0,988 0.5000 0.5018 3.153 0,996 11,68 11,73 0.512 0.990 0,5500 0,5511 3,463 0.998 15,93 15,96 0.507 0,994 0.6000 0.6006 3.774 0,6500 0,6504 4.086 0.999 29.75 29.77 0,502 0.999 21,76 21,79 0.504 0.997 0,998 0.7000 0,7002 4.400 1,000 40.70 40,71 0.501 0,999 0.7500 0.7501 4,713 1,000 55,70 55.71 0.501 0,8000 0.8001 5.027 1.000 76,23 76,24 0.500 0,8500 0.8500 5.341 1,000 104.4 104.4 0.500 0.9000 0.9000 5,655 1.000 142,9 142,9 0.500 0.9500 0.9500 5.969 1.000 195,6 195.6 0.500 1.0000 0.999 1.000 1.000 1.000 1.000 1.0000 6.283 1.000 267.8 267,8 0,500 1.000 Linear wave theory, table of functionsSee Answer
Q2: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 σ = √2/π 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 = Hmov-2 In U where U is a random number between 0 and 1. Wave period: =3+7*RAND() 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 Hs = 6 m. What is Hmax such that there is only a 5% chance it will be exceeded?See Answer
Q3:(12%) Problem 7: The captain of a crab boat on the coast of Alaska notes that in a time period of t = 15 minutes, the boat goes up and down n = 29 times. Randomized Variables t = 15 minutes n = 29 f= 33% Part (a) Input an expression for the frequency of the ocean wave, f. a FOR 0 h k P Submit B f i m S Hint R tra j n t M 741 * 8 9 6 ^^ 4 1 + 0 VO BACKSPACE 52 ه | نیا 3 Feedback I give up! HOME Allanton30245xor To LLC END CLEAR Hints: 0% deduction per hint. Hints remaining: 1 A 33% Part (b) What is the frequency, in hertz? A 33% Part (c) If the crests are d = 100.0 m apart how fast are the waves traveling in meters per second? Feedback: 0% deduction per feedback. Grade Summary Deductions Potential 0% 100% Submissions Attempts remaining: S (5% per attempt) detailed viewSee Answer
Q4:9:00 PM End Date: 1:59:00 PM (8%) Problem 5: Sound travels at a speed of v= 1530 m/s in water. While underwater a student hears a f= 2.5 kHz note in a whale song. Randomized Variables v=1530 m/s f=2.5 kHz λ= 50% Part (a) Input an expression for the wavelength of the sound wave in water 2. Hints: 0% deduction per hint. Hints remaining: 1 a a g k S Submit 50% Part (b) What is the wavelength in meters? PE d h m t Hint 0 f j P V ( ) 7 8 1시 시 * 7 9 HOME 5 6 4 1 2 3 + 0 VO BACKSPACE O Feedback END CLEAR I give up! Feedback: 0% deduction per feedback. Grade Summary Deductions Potential 0% 100% Submissions Attempts remaining: 5 (5% per attempt) detailed view/n(16%) Problem 6: A student attaches a f= 2.5 kHz oscillator to one end of a metal rail of length L=14 m. The student turns on the oscillator and uses a piezoelectric gauge at the other end to measure that the resulting sound wave takes t = 0.0063 s to travel the length of the rail. DA 25% Part (a) Input an expression for the period of the waves in the rail, in terms of the given quantities. T= B 0 f j n Submit Y b g k P Hint Л d h m S ( ) 7 8 9 ^^^ 4 5 6 * 1 2 3 0 + VO BACKSPACE Feedback Hints: 0% deduction per hint. Hints remaining: 1 A 25% Part (b) What is the period, in seconds? 25% Part (c) What is the speed of the wave in the rail, in meters per second? A 25% Part (d) What is the wavelength of the wave within the rail, in meters? HOME I give up! Feedback: 0% deduction per feedback. All mot 1074 HT 110 7 END DEL LEAR Grade Summary Deductions Potential 0% 100% Submissions Attempts remaining: 5 (5% per attempt) detailed viewSee Answer
Q5:(8%) Problem 4: A student observing the ocean notes that n = 7 crests break in 1 = 3.8 minutes? f= 50% Part (a) Input an expression for the frequency of the waves. Hints: 0% deduction per hint. Hints remaining: 1 n 0 60 g j P Submit 50% Part (b) What is the frequency in hertz? a a h k S Hint В d i m t ) ^^^ * 7 8 9 4 5 6 1 2 3 + - VOBACKSPACE 0 Feedback DEL. HOME END CLEAR I give up! Feedback: 0% deduction per feedback. Grade Sun Deductions Potential Submission Attempts re (5% per atte detailed vieSee Answer
Q6:(4%) Problem 3: The wavelength is a fundamental property of a mechanical wave. Which of the following is true about the wavelength of a mechanical wave? It is the distance from crest to trough. Hints: 0% deduction per hint. Hints remaining: 1 It is the distance over which a vibration repeats itself. It measures the distance that the medium has travelled. It can be divided by a frequency to determine speed. Feedback I give up! Submit Hint Feedback: 0% deduction per feedback. Gra Ded Pote Sub Atte (33 detaSee Answer
Q7:Lesson 6 Wave Properties Begin Date: 2/26/2024 12:01:00 AM -- Due Date: 3/10/2024 11:59:00 PM End Date: 5/12/2024 11:59:00 PM (4%) Problem 2: A "mechanical wave" occurs in a physical medium because of some restoring force acting on the medium, and can be described by an amplitude, an oscillation, and a frequency. A You can easily decrease the wavelength of a mechanical wave by half by doubling the frequency ONLY if which of the following is true? Select all that apply. The amplitude is doubled Grade Summary The same medium is used at the same temperature Deductions. Potential The ratio between the restoring force and the density of the medium remain constant. The amplitude is reduced by 1/2 Hints: 0% deduction per hint. Hints remaining: 2 Submit Hint I give up! Feedback: 0% deduction per feedback. Feedback 0% 100% Submissions Attempts remaining: 5 (5% per attempt) detailed viewSee Answer
Q8:(8%) Problem 1: This problem will ask about some of the basic characteristics of waves. A 50% Part (a) Which of the following are true about traveling waves? Select all that apply. Waves must have an amplitude, wavelength, and frequency. Traveling waves transport energy. Traveling waves are modeled as some sort of "disturbance" that travels away from its source. Waves must exist in a medium. Hints: 0% deduction per hint. Hints remaining: 1 Submit Hint Feedback I give up! Feedback: 0% deduction per feedback. A 50% Part (b) Which of the following are true about all mechanical traveling waves? Select all that apply. 00345 TL 116 Grade Summary Deductions Potential 0% 100% Submissions Attempts remaining: 5 (5% per attempt) detailed view/n) Problem 1: This problem will ask about some of the basic characteristics of waves. A 50% Part (a) Which of the following are true about traveling waves? Select all that apply. A 50% Part (b) Which of the following are true about all mechanical traveling waves? Select all that apply. They must have intensity. They are created by particles that are disturbed from their equilibrium positions/state. They transfer energy. They must have an amplitude, wavelength, and frequency. Hints: 0% deduction per hint. Hints remaining: 1 Submit Hint Feedback I give up! Feedback: 0% deduction per feedback. Grade Summary Deductions Potential 0% 100% Submissions Attempts remaining: 5 (5% per attempt) detailed viewSee Answer
Q9:4) A physical quantity, y(x,t), is a function of distance x and time t, and also obeys the wave equation: a²y at² and a²y əx² c². 0. where c is a wave speed. (a) What is a general solution to this wave equation? (b) The initial conditions on the y variable is given by the functions: y(x,t=0) = cos(2x) for -π/4 <x<+/4; and y =0 for other x values. dy/dt(x,t=0) = 0. What is the wave solution, y(x,t)? Sketch y(x,t) at a few times.See Answer
Q10:Q3. V ~N Square wave Sinusoidal Triangular wave Our power supply generates above three wave forms at 250 Hz with Vp=3.5 V and a DC offset 2.5 V: 1. Draw each wave form on the V-t graphs below. 2- 0- 2- 2. Determine Vave for each wave form - 2- 3. Determine Vrms for each wave form (write the math formula you used for calculation).See Answer
Q11: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
Q12: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
Q13: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
Q14: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
Q15:1. 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
Q16:1. 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
Q17:1. 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
Q18:4. 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
Q19:3. 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
Q20:English (United States) 1. Jamie and Addy are driving in their car in the school parking lot. While they are driving Addy decides to play his clarinet out of the window of the car. A student they are driving away from at a speed of 8.5 m/s hears a frequency of 640 Hz. (The Speed of sound is 341 m/s) a) What was the frequency of the note played on the clarinet? b) How fast would they have to drive away from the student so that they hear a frequency of 600 Hz? Student observationSee Answer

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