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Verify by direct substitution that the wave function for a standing wave given in Equation 17.1,
is a solution of the general linear wave equation, Equation 16.27:
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Chapter 17 Solutions
PHYSICS FOR SCI.AND ENGR W/WEBASSIGN
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- Question 19 A string hanging from a shelf supports aarrow_forwardA transverse wave traveling along an x axis has the fornm given by (16-18) y =y," sin(kx ± ω1 + φ). Figure 16-8a gives the displacement of string elements as a function of , al at time0. Figure 16-8h gives the displacements of the element at x 0 as a function oft. Find the values of the quantities shown in Eq. 16-18, including the correct choice of sign. (min) 10 20 -10 -20 -9 *レ b)arrow_forwardAn E&M wave has an e-field given by E(x,t) - -(4.950V/m)k cos(ky + (1.38 x 101 rud/)t) Which of the following is correct for B(x, t) and the direction of propagation? (c - 3x10 m/s) B(7, t) - -(0.165 NA)i cos ((4.6 x 10° rad/m)y + (1.38 x 1015 rad/)e),y B(x, t) - (33.0 nT)j cos (2.3 x 10*rad/m)y + (2.78 x 101 rad/s)e). - d/m)y + (1.38 x 10 rad 1. I. rad/).-y B(x, t) = (11.5 aT)t cos ((4.6 x 10 rad/mly + (1.38 x 10 rad (1.38 x 101 rad, /,). -y. B(x, t) - (16.5 nT)t cos ((4.6 x 10* rad II. IV. IV None of the abovearrow_forward
- Consider the one-dimensional wave equation Pu u 0<<1, t20 u(0, t) = u(1, t) = 0 u(x, 0) = 3 sin(27x) du (x, 0) = x – x². Use CTCS scheme with Ar = 0.1, At = 0,05 to estimate the value of the displacement u(0.9,0.15).arrow_forwardExample 14-8 depicts the following scenario. Two people relaxing on a deck listen to a songbird sing. One person, only 1.66 m from the bird, hears the sound with an intensity of 2.86×10−6 W/m^2. A bird-watcher is hoping to add the white-throated sparrow to her "life list" of species. How far could she be from the bird described in example 14-8 and still be able to hear it? Assume no reflections or absorption of the sparrow's sound.arrow_forwardA traveling wave is described by y = 10 sin (βz – ωt). Sketch the wave at t = 0 and at t = t1, when ithas advanced λ /8, if the velocity is 3 X 108 m/s and the angular frequency ω = 1 X 106 rad/s. Repeat for ω = 2 X 106 rad/s and the same t1.arrow_forward
- Given the wave functions y1 (x, t) = A sin (kx − ωt) and y2 (x, t) = A sin (kx − ωt + ϕ) with ϕ ≠ π/2 , show that y1 (x, t) + y2 (x, t) is a solution to the linear wave equation with a wave velocity of v = √(ω/k).arrow_forwardAt high frequencies, the value of the propagation constant (y) is approximately :* Y = (R + j@ L ) ( G + j w C ) Y = a Option 4 Option 3 Y = a +jß Y = j ß Option 1 Option 2arrow_forwardO F= 9f A traveling wave on a taut string with a tension force T is given by the wave function: y(x,t) = 0.1sin(2tx-300t), where x and y are in meters and t is in %3D seconds. The linear mass density of the string is u = 100 g/m, and the string is 5 m-long. The total energy on the string is O 90 J O 225 J O 450 J 45 J O 22.5 J -rhy thewevearrow_forward
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