Consider a lattice of 27 sites in a cubical arrangement. each lattice site contains an electron. given the following rules, provide a description (graphical, mathematical, or computational, etc.) of the arrangement of electron spins in the lattice for minimum and maximum entropy configurations, entropy in each case. expression for the as well as an rule a: the electron shares a spin identical to at least two neighboring electrons rule b: the electron shares a spin identical to at least one rule c: the electron shares a spin opposite to at least two neighboring electrons. rule d: the electron shares a spin opposite to at least one neighboring electron. neighboring electron

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒