In: Physics
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). |