By Alvin Halpern, Erich Erlbach

AKA: Schaum's define of Preparatory Physics II : electrical energy and Magnetism, Optics, glossy Physics

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**Extra resources for Beginning Physics II: Waves, Electromagnetism, Optics and Modern Physics**

**Example text**

1) where A is an arbitrary number. Integer Powers of a Number When the exponent, x, is a positive integer we have the usual powers of A : A1 \ A ; A2 \ A É A ; A3 \ A É A É A, etc. By convention, A0 \ 1. For negative integers we deÐne A~1 \ 1/A ; A~2 \ 1/A2 and in general : A~n \ 1/An \ (1/A)n. Clearly, by examination of a few simple examples, we have for any two non-negative integers : An É Am \ A(n`m) ; An É A~m \ An~m. 2) where now n and m are any positive, negative or zero integers. 1. Show that for any two non-negative integers, n and m : (a) (An)m \ (Am)n \ A(n Õ m) (b) An É A~m \ A~n É Am \ A~(n Õ m) Solution (a) This can be shown by generalizable example.

Beg. Phys. 7). PV \ nRT \ mRT /M Then : (ii) Dividing both sides by V , and noting that o \ m/V , we get : P \ oRT /M (iii) Substituting (iii) into (i) we get : v \ [cRT /M]1@2, which is the desired result, Eq. 15). 7. 40, respectively. 013 É 105 Pa. A (a) Calculate the velocities of sound in hydrogen and helium at P \ P and T \ 300 K (27 ¡C). A (b) Calculate the velocity of sound in air at P at : T \ 273 K, T \ 300 K, and T \ 373 K. 0 kg/kmol. air Solution (a) Using Eq. 0 kg/kmol)]1@2 \ 1020 m/s.

1-12, the vertical arrows indicate the relative direction of the transverse motion of molecules in the cord between successive pairs of nodes). 24. 60 m, and mass m \ 160 g is under tension S \ 200 N. 23. (a) Find the three longest resonant wavelengths for the rope. (b) Find the fundamental frequency and Ðrst two overtones for resonant standing waves in the rope. (c) How would the results to part (a) and (b) change if the tension in the rope were 800 N ? 40 m. 2 3 CHAP. 1] (b) (c) 25 WAVE MOTION From Eqs.