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- 38. Using the general properties of the harmonic-oscillator wave functions y(x), evaluate the following integrals: +00 (a) (vs]ys) = [y*(x)¥¸(x)dx -00 +00 (b) (y₁]ys) = [y*(x)¥¸(x)dx -00An E&M wave has an e-field given by E(x, t) = -(4.950V/m)k cos(ky + (1.38 × 1013 rad/ s)e). %3D Which of the following is correct for B(x,t) and the direction of propagation? (c = 3x10$ m/s) B(x, t) = -(0.165 µA)î cos (4.6 x 106 rad/m)y +(1.38 x× 1013 rad/s)t),y I. т B(x, t) = (33.0 nT)j cos ((2.3 × 10ª rad/m)y + (2.78 × 1013 rad/3)t),–x I. B(x, t) = (16.5 nT)î cos ((4.6 x 10* rad/m)y + (1.38 × 1013 rad/s)t),-y II. IV. B(x, t) = (11.5 µT)î cos ((4.6 × 10² rad 4.6 × 10² rad/m)y + (1.38 × 1013 rad/s)t),-y. II II O IV None of the aboveCalc based physics The general wave function on a string is given by : Y(x,t) = Acos(Kx+wt+Q). Prove that the ratio of d2Y/dt2 over d2Y/dx2 is (w/k)2. Prove that w/k represents velocity.
- An interface is formed between a block of aluminium (with an acoustic impedance of 1.8 x 107 kg m2 s') and a block of copper (with an acoustic impedance of 4.6 x 107 kg m-2 s-1). Longitudinal sound waves travelling through the aluminium are normally incident on the boundary, and are partially reflected. a) What is the ratio of the amplitude of the reflected wave to that of the incident wave? Number b) What is the ratio of the amplitude of the transmitted wave to that of the incident wave? Number c) What percentage of the incident power is transmitted? Number d) What percentage of the incident power is reflected? Number % Ouit P Sove QuestiondeShow by direct substitution that the exponential Gaussian function defined by ?(x,t) = ae-(bx-ct)^2 satisfies the wave equation: (?2?(?,?))/(?x2) = (1/v2) * (?2?(x,t))/(?t2) if the wave is given by the v = (c/b) and a, b, and c are constants.