R 7 will nger sent SECTION 7.2 (Classical Standing Waves) your answer to explain clearly why the w itself if we move from any point xo to Xo fixed). Show similarly what happens if w from any to to to + T. 7.1 . A string is oscillating with wave function t an y(x, t) = A sin kx cos ot her (7.118) e by om the ctly es. ed with A 3 cm, k = 0.2m rad/cm, and o For each of the times t = 0, 0.05, and 0.07 s, sketch the string for 0 x 10 cm. 10TT rad/s. A string is oscillating with wave fun 7.9 2.5 cm, k 1 form (7.118) but with A www.d 10TT rad/s. (a) Sketch two complete of the wave at each of the times t = t=0.1 s. (b) For a fixed value of x, (7.118) with respect to t to give the string velocity at any position x. Graph this function of x for each of the two times in K 22 A standing wave of the form (7.118) has amplitude 7.2 2 m, wavelength 10 m, and period T 2s. Write down the expression for y(x, t) E71 4 7.3 A string is clamped at the points x = 0 and x= 30 cm. It is oscillating sinusoidally with amplitude 2 cm, wavelength 20 cm, and frequency f = 40 Hz. Write an expression for its wave function y(x, t). SECTION 7.3 (Standing Waves in Quant Mechanics) 7.10 Prove that any complex number z = and y real) can be written as z re" real). Give expressions for x and y in te and vice versa. [Hint: Use Euler's form For the standing wave of Eq. (7.118) calculate the string's transverse velocity at any fixed position x. [That is, differentiate (7.118) with respect to t, treat- ing x as a constant.] At certain times the string's dis- placement is zero for all x, and an instantaneous 7.4 7.11 (a) Show for any complex numbe that z2zz where z = x - iy is conjugate of z. (b) Hence, prove the snapshot of the string would show no wave at all. and indicate. with

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter5: Matter Waves

Section: Chapter Questions

Problem 35P

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