Kevin Zhou — USAPhO Practice — Modern Problem 3 · Kevin Zhou #USAPhOX.3
Physics · modern-physics
Problem
Given that the lowest frequency component present in the multiplied signal is f = 4.8kHz,
low
calculate the speed of the car v.
You may find it useful to use the trigonometric identity
cosαcosβ = (cos(α+β)+cos(α−β))/2.
Question A2
Wood burns in a fireplace on the ground, producing smoke with temperature T = 40◦C, which
1
slowly rises through the atmosphere. Neglect the exchange of heat between the smoke and the
surrounding air, and suppose the atmosphere has pressure p = 100kPa at the ground, and uniform
0
temperature T = 20◦C. Treat both the smoke and atmosphere as diatomic ideal gases of molar
0
mass µ = 29g/mol, and recall that 0◦C = 273K. To within 10%, how high does the smoke column
rise?
Question A3
Consider a particle of mass m confined to a one-dimensional box of length L. We consider the
quantum mechanics of this system. For simplicity, express your answers in terms of the quantity
α = h2/8m as much as possible.