Consider the function f(x) = cos (bx2), where b = 0.0628cm−2. PLEASE SHOW ALL WORK AND...

Consider the function f(x) = cos (bx²), where b = 0.0628cm⁻². PLEASE SHOW ALL WORK AND EXPLAIN THOROUGHLY!

Equation Q12.8: [λx]2=-4π2f(x)d2f/dx2

(a)	Argue that this function has crests at x = 0, 10 cm, 14.1cm, 17.3 cm, 20 cm, 22.4 cm, and so on.
(b)	Draw a graph of this function and show that it is like a wave whose wavelength decreases as x increases.
(c)	Estimate this function’s local wavelength at x = 20cm by averaging the distances to adjacent crests on either side of this point.
(d)	Compute this function’s local wavelength at x = 20cm, using equation Q12.8, and compare the result with your answer for part (c).

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Expert Solution

genius_generous answered 1 year ago

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