Modern Physics For Scientists And Engineers
Modern Physics For Scientists And Engineers
2nd Edition
ISBN: 9781938787751
Author: Taylor, John R. (john Robert), Zafiratos, Chris D., Dubson, Michael Andrew
Publisher: University Science Books,
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Chapter 7, Problem 7.4P
To determine

String’s transverse velocity.

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Show that a gaussian psi (x) = e ^(-ax^2) can be an eigenfunction of H(hat) for harmonic oscillator 1. Compute T(hat)*psi 2. Compute Vhat* psi - assume V operator is 1/2w^2x^2 3. Write out Hbar*psi and identify terms so Hber*psi=E*psi is true 4. From cancellation find a 5. insert back a to Schrodinger eq above and find E
Sketch f(y) versus y. Show that y is increasing as a function of t for y < 1 and also for y > 1. The phase line has upward-pointing arrows both below and above y = 1. Thus solutions below the equilibrium solution approach it, and those above it grow farther away. Therefore, ϕ(t) = 1 is semistable.
Describe whether the beating frequency increases or decreases when the difference in frequency between two sources of vibration is reduced. Justify your answer. Sketch the dependency between the Compliance of a Helmholtz resonator, C, and the volume of the body of the resonator, V. Calculate a wavelength of sound that would be transmitted with minimal loss through a Low-Pass acoustic filter that has a middle section of length, L = 15 cm.

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