3a.3. Consider a longitudinal wave us propagating in a linear monoatomic chain of mass M and...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
3a.3. Consider a longitudinal wave us propagating in a linear monoatomic chain of mass M and with lattice spacing a and the nearest neighbor interaction C. us = u cos(wt - ska) a) Show that the total energy (summed for all particles) is given by, 2 Erotal = K + U = [/2M (dus) = [ { M (+)² + Σ ² C(U²₁ - 1₂+₂) us+132 S b) Show that the dispersion relation is given by dispersion relation 4C = M Ka |sin (1) @= c) time-averaged total energy per atom is 1 1 Eaug = Ma²u²+ C(1-cosKa)u² = Mw²u² Savg = = 3a.3. Consider a longitudinal wave us propagating in a linear monoatomic chain of mass M and with lattice spacing a and the nearest neighbor interaction C. us = u cos(wt - ska) a) Show that the total energy (summed for all particles) is given by, 2 Erotal = K + U = [/2M (dus) = [ { M (+)² + Σ ² C(U²₁ - 1₂+₂) us+132 S b) Show that the dispersion relation is given by dispersion relation 4C = M Ka |sin (1) @= c) time-averaged total energy per atom is 1 1 Eaug = Ma²u²+ C(1-cosKa)u² = Mw²u² Savg = =
Expert Answer:
Related Book For
Posted Date:
Students also viewed these physics questions
-
Consider particles of mass m and energy E moving along the x-axis under the influence of a potential V(x). The particles have energy E > 0 and the potential had the from V(x) = 0 for x < 0, V(x) = V0...
-
Consider an oil droplet of mass m and charge q. We want to determine the charge on the droplet in a Millikan-type experiment. We will do this in several steps. Assume, for simplicity, that the charge...
-
A hoop of mass m and radius r starts from rest and rolls down an incline at an angle . The hoop's inertia is given by IG = mr2. The static friction coefficient is s. Determine the acceleration of the...
-
Calculate the density of N2 at STP, (a) using the ideal-gas law and (b) using the molar volume and molar mass of N2. How do the densities compare?
-
A horizontal cable supports the boom of a crane. If the tension in the cable is 4500N and the crane is supporting a 7500-N girder, what is the compression in theboom? 1.00 m 1125 N
-
Records over the past year show that 1 out of 350 loans made by Mammon Bank have defaulted. Find the probability that 2 or more out of 300 loans will default. Is it appropriate to use the Poisson...
-
Chocolate Inc. began 2007 with cash of \($55,000.\) During the year Chocolate Inc. earned revenue of \($600,000\) and collected \($620,000\) from customers. Expenses for the year totaled...
-
Commercial banks moved heavily into equipment leasing during the early 1970s, acting as lessors. One major reason for this invasion of the leasing industry was to gain the benefits of accelerated...
-
2009 2010 2011 2012 A. Currency 920 930 932 937 B. Money market mutual fund shares 677 682 680 689 C. Saving account deposits 5,700 5,980 6,168 6,305 D. Money market deposit accounts 1,205 1,236...
-
Prove that Ki = xCi (x mi)(m mi) = 0. This fact was used in the proof that TSS = SSE + SSB on page 557.
-
Name of the company: NIKE INC. BALANCE SHEET Report date : MAY 31,2019 & 2018 a. Answer the following questions. Use complete sentences, and explain your answers by reference to the information you...
-
Required Compute variances for the following items and indicate whether each variance is favorable (F) or unfavorable (U): Note: Select "None" if there is no effect (i.e., zero variance). Item Sales...
-
1.Taxpayer, a cash method, calendar year taxpayer, engaged in the following transactions in shares of stock. Consider the amount and character of T's gain or loss in each transaction: (a)T bought 100...
-
Use the information provided below to calculate the following independently: 1.3.1 1.3.3 Net profit Marginal income per unit that will enable the project to break even 1.3.2 Break-even quantity if...
-
Suppose that China and Germany each have 1,000,000 labour hours available for the pro- duction of cell phones and computers. The number of labour hours needed to produce cell phones and computers in...
-
How do I use voice commands to control my computer with the project of making a video?
-
ALL IP addresses must contain a value (octet) that is unique to your group. Point-to-point links must use a /30 mask, all other networks use /24 Internal Point-to-point links (Backbone) wil use...
-
Explain the regulation of the secretions of the small intestine.
-
Filling sub bands for electrons in a square GaAs wire of width 20 nm, find the linear electron density at which the n x , = 2, n y , = 2 sub band is first populated in equilibrium at T = 0. Assume an...
-
Form factor of atomic hydrogen for the hydrogen atom is its ground state, the number density is n(r) = (a 0 3 ) 1 exp ( 2r/a 0 ), where a0 is the Bohr radius. Show that the form factor is f G = 16/...
-
Para-magnetism of S = 1 system. (a) Find the magnetization as a function of magnetic field and temperature for a system of spins with S = 1, moment and concentration n. (b) Show that in the limit B...
-
Describe the process of valuing the entrepreneurs ownership interest in a two-stage investment. Refer to Tables 13.10 and 13.13. Data from table 13.10 Data from table 13.13 Market potential...
-
Euro Exchange Rates. The exchange rate that we consider is the amount of euros that one can purchase for one U.S. dollar. We have \(T=699\) daily observations from the period April 1, 2005, through...
-
Evaluate the current yield curve level and structure using the following screens: a. YCRV or GC to access yield curves. b. FWCV to determine implied forward rates. c. USoo03M, USoo06M, USoo09M, and...
Study smarter with the SolutionInn App