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Does an automobile radio antenna vibrate in resonance due to vortex shedding? Consider an antenna of length L and diameter D. According to beam vibration theory [see [34] or [35, p. 401]], the first mode natural frequency of a solid circular cantilever beam is
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- Ultrasonic sound waves are often used in methods of nondestructive testing. For example, this method can be used to find structural faults in a steel I-beams used in building. Consider a 10.00 meter long, steel I-beam with a cross-section shown below. The weight of the I-beam is 3846.50 N. What would be the speed of sound through in the I-beam? (Ysteel = 200 GPa, βsteel = 159 GPa).arrow_forward2) A wave in a depth d = 12 m, height H = 3 m, and a period T = 10 sec. The corresponding deepwaterwave height is H0 = 3.13 m.Find:(a) The maximum horizontal and vertical displacement of a water particle from its mean position when z= 0 and z = -d.(b) The maximum water particle displacement at an elevation z = -7.5 m when the wave is in infinitelydeep water.(c) For the deepwater conditions of (b) above, show that the particle displacements are small relative tothe wave height when z = -L0 /2arrow_forwardAs shown in the figure below, a string attached to a vertical wall passes over a pulley at the end of a horizontal rod, and supports a sphere. The horizontal rod has a length L = 0.320 m, the mass of the sphere is M = 1.20 kg, the string makes an angle ? = 38.0° with the rod, and, when the string is plucked, the fundamental frequency of standing waves in the portion of the string above the rod is f = 70.0 Hz. Determine the mass of the portion of the string above the rod (in g). Answer:___________ garrow_forward
- Consider two sinusoidal sine waves traveling along a string, modeled as y1 (x, t) = 0.3 m sin (4 m−1 x − 3 s−1 (t)) and y2 (x, t) = 0.3 m sin (4 m−1 x + 3 s−1 (t)). What is the wave function of the resulting wave? [Hint: Use the trig identity sin(u ± v) = sin u cos v ± cos u sin varrow_forwardIn certain area in the ocean, its density is 1000 kg/m3, the tidal wavelength of 700 km,wave height of 150m, water depth of 275m and wave period of 8 s. Find the following: d. Wave power over a width 300m.arrow_forwardA 3.00m long steel wire is fixed in a ceiling and a mass of 12.3kg is hanging from the wire. The wire has a diameter d=0.80mm, a Young’s modulus 2.00GPa and mass density 7860kg/m^3 d) Calculate the transverse speed of pulse e) calculate the longitudinal sound speedarrow_forward
- Specifically a dynamics problem. Question and diagram in pics below. Apparently the answers are aB=-24.86 j ft/s2 and alpha=1.47 rad/s2.arrow_forwardhow did you get the value on wien's displacement law. explain. thanks.arrow_forwardA wire of length L1=30cm has a fixed end and the other end is welded to another wire, whose linear mass density is 4 times smaller. The second wire passes over a pulley and a mass of 10kg is suspended from its other end.The distance L2 between the welding point and the pulley is 80 cm. A standing wave is produced in the composite wire, whose ends on the left wall and on the pulley remain fixed.If the frequency is as low as possible and there is a node at the weld spot, what is the number of nodes in this standing wave, including nodes on the left wall and on the pulley?a)3b)4c)5d)6e)7f)8g)9h)10i)11j)12k)13l)14m)15arrow_forward
- Find the natural frequency (in Hertz) of the system illustrated in the following figure. Consider the length of the rigid bar as 2L, the mass of the rigid bar as m and assume K1=6,580 N/m, K2=7,635 N/m, M=1.9 kg, m= 3 kg, L=0.5 m and g=9.81 m/s2.arrow_forwardA flexible string 1.0 m long is connected to an oscillator. When the oscillator is set to vibrate the string at 100Hz, a standing wave is formed in the fundamental mode of oscillation. What is the speed of waves on the string?arrow_forwardA 0.1kg object oscillator as a simle harmonic motion along the x _axis with a frequency f=3.18 hz at a position x1,the object has a kinetic energy 0.7j and a potential energy 0.3j,the amplitude of oscillation A is:arrow_forward
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