Th of temperature 10. Imagine a piano wire of mass M, under tension F, between fixed point we assume that the displaceme

[answerhappygod]

Th Of Temperature 10 Imagine A Piano Wire Of Mass M Under Tension F Between Fixed Point We Assume That The Displaceme 1 (70.76 KiB) Viewed 32 times

Th of temperature 10. Imagine a piano wire of mass M, under tension F, between fixed point we assume that the displacement of the wire from equilibrium occurs or distance L apart. The wire at rest lies along the x axis. To simplity matum along the y direction. Thus y(0) = y(L) since there is no ends of the wire. The energy of the wire for an instantaneous displacement y(x,t) is Th to th th at the ,) = 13 0 +/* a(++)) Ely(x, t)) = 1 da м(ду Lat F ar ay ar We write y(x, t) as the Fourier series N пТТ 12. S y(,t) = An(t) sin ("7"). L n=1 Show that the energy can be written as ) Σ(Μας + CY****** Ely(x, t)) = A2 4L n=1 Treat An and An as a set of 2N generalized coordinates which define the instantaneous position of the wire. (a) Calculate the average thermal energy of the wire under tension, and hence obtain its heat capacity. (b) Determine the average value of An, of Am, and of An An, with n #n'. (c) Express the mean square y(x, t)2 in the form of a sum of some quantity over n. From this determine the mean square displacement of the wire at I = L/2. [You may use without proof the relation main-2 = 72/8. 11. Elementary excitations in sunului 1