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A wave traveling along a string is given by
where x is the distance along the string in meters and y is the vertical displacement. Determine: (a) the direction of wave travel, (b) the reference phase ϕ0, (c) the frequency, (d) the wavelength, and (e) the phase velocity.
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Chapter 1 Solutions
Fundamentals Of Applied Electromagnetics
- A plane electromagnetic wave with frequency f = 5 MHz is propagating in sea water ( er = 72, mr = 1, and s = 4 S/m). Find: the loss tangent the attenuation constant the phase constant the intrinsic impedance the phase velocity the wavelength the “skin depth” the distance for which the electric field decreases to 1% of its value at the surfacearrow_forwardThe parameters of a certain undistorted transmission line operating at 12 MHz are L = 0.4 μH/m, C = 40 pF/m, and R = 20 Ω/m. If the wave travels 5m, what is its phase shift at this distance? (write it in radians)arrow_forwardAt a frequency of 200 MHz, a plane electromagnetic wave propagates in the x direction. What is the instantaneous expression of the electric field component with amplitude of 1 V/m? ax, ay, az are the unit vectors in the x, y, z directions, respectively. The "^" symbol represents the exponential operation. eg. 2^3 means 2 to the power of 3. ay.cos(4*pi*10^8*t-x*4*pi/3) V/m ax.cos(2*pi*10^8*t-y*2*pi/3) V/m ax.cos(4*pi*10^8*t-y*4*pi/3) V/m ay.cos(2*pi*10^8*t-x*2*pi/3) V/marrow_forward
- In free space, H = 0.1 cos(2*10^8t-kx)ay A/m.(a) Calculate k, l(lambda), and T.(b) Calculate the time t1 it takes the wave to travel l(lambda)/8.(c) Sketch the wave at time t1. footnote ; I =LAMBDAarrow_forwardA source emitting electromagnetic signals with a natural frequency of ω0=3.0⋅1010rad / s moves at a constant speed v=0.80 s in a straight line, spaced from a stationary observer P at a distance ll (Fig.). Find the frequency of the signals perceived by the observer at the moment when: a) the source will be at point O; b) the observer will see it at point O.arrow_forwardTrue or False. 1. If the propagation constant is complex valued, E and H does not attenuate and are in-phase. 2. In general, when electromagnetic wave propagates in any media, the EM wave does not attenuate and the electric and magnetic fields are out-of-phase. Please explain.arrow_forward
- A piano wire with a mass of 2.75 g and a length of 85 cm is stretched with a tension of 30 N. A wave with frequency 135 Hz and amplitude 1.8 mm travels along the wire. Calculate the average power carried by the wave.arrow_forward1- Think of three electrical appliances that are used at home. What kind of waves are produced in these electrical appliances? 2- Have you ever built a telephone with two glasses and a thread? Build one and explain how waves are presented in this apparatus. 3- How do you consider that the study of waves has allowed the technological development of society? 4- Bats use ultrasound waves to see. How has science used this concept to create technological gadgets?arrow_forwardAn electromagnetic wave in free space is propagating along the z-direction and its electric field is polarized in the +y-direction. The frequency of the wave is 500 MHz, and the maximum amplitude of 10 mV appears at z = 10 m. Write the instantaneous equations for the electric field and magnetic field intensities. Complete solution pleasearrow_forward
- A 1.3 GHz uniform wave of amplitude EX0 of 100 V/m at the origin is propagating in the z direction. The medium of propagation has the following parameters ε''=10 x10-11 F/m, ε'=1x10-11 F/m and μ=3x 10-6H/m. Find the instantaneous expression for the electric field.arrow_forwardThe magnetic field of a wave propagating through a certain nonmagnetic material in the positive y direction has an amplitude of 30 mA/m and a frequency of 1082π1082πHz . If the wave is polarized on the positive z direction and its wavelength is 12.6 meter, find the equation of the instantaneous Electric field. Assume the initial phase is 0.arrow_forwardTwo sinusoidal waves of wavelength λ = 2/3 m and amplitude A = 6 cm and differing with their phase constant, are travelling to the right with same velocity v = 50 m/s. The resultant wave function y_res (x,t) will have the formarrow_forward
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