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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 Scientists And Engineers
- A copper wire has a density of =8920 kg/m3, a radius of 1.20 mm, and a length L. The wire is held under a tension of 10.00 N. Transverse waves are sent down the wire. (a) What is the linear mass density of the wire? (b) What is the speed of the waves through the wire?arrow_forwardTwo sinusoidal waves are moving through a medium in the positive x-direction, both having amplitudes of 7.00 cm, a wave number of k=3.00 m-1, an angular frequency of =2.50 s-1, and a period of 6.00 s, but one has a phase shift of an angle =12 rad. What is the height of the resultant wave at a time t=2.00 s and a position x=0.53 m?arrow_forwardVerify by direct substitution that the wave function for a standing wave given by: y= (2A cos kx) cos wt is a solution of the general linear wave equation: 1 a?y ax?arrow_forward
- Show that a standing wave given by the equation: y (x, t) = A sin (kx) sin (ωt) satisfies the wave equation, verify that: v0 = ω / k; shows that the standing wave also satisfies the equation of harmonic oscillator: ∂2y(x,t)/∂t2 = −ω2y(x,t), interpret this result.arrow_forwardQuestion 19 A string hanging from a shelf supports aarrow_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
- A 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_forwardConsider 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_forward
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