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Test 1 Questions for Wave Motion and Optics | PHY 315, Exams of Physics

The University of Texas at AustinPhysics
Prof. Richard Fitzpatrick

Material Type: Exam; Professor: Fitzpatrick; Class: WAVE MOTION AND OPTICS; Subject: Physics; University: University of Texas - Austin; Term: Spring 2010;

Typology: Exams

Pre 2010

Uploaded on 05/06/2010

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Physics 315: Oscillations and Waves
Midterm 1. Answer all questions. Give reasons for your answers.
1. A mechanical system with one degree of freedom oscillates about a stable
equilibrium state. Its displacement from the equilibrium, x(t), satisfies the
simple harmonics oscillator equation:
d2x
dt2+ω2x= 0.
(a) What is the physical significance of the quantity ωappearing in the
above equation?
(b) What is the characteristic period of the oscillation?
(c) Write a solution to the above equation for which x(0) = 0 and ˙x(0) = v.
(d) Demonstrate that
E= ˙x2+ω2x2
does not vary in time. What is the physical significance of E?
2. Consider a one-dimensional wave in a uniform medium. Suppose that the
wave disturbance, y(x, t), satisfies the wave equation
∂2y
∂t2=v2∂2y
∂x2.
(a) What is the physical significance of the quantity vappearing in the
above equation?
(b) What is the dispersion relation for standing waves? Define all terms
in your answer.
(c) What is the dispersion relation for traveling waves?
(d) Write an expression for a standing wave solution of peak amplitude A
and angular frequency ω. What are the wavelength and period of the
wave?
pf2

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Download Test 1 Questions for Wave Motion and Optics | PHY 315 and more Exams Physics in PDF only on Docsity!

Physics 315: Oscillations and Waves Midterm 1. Answer all questions. Give reasons for your answers.

  1. A mechanical system with one degree of freedom oscillates about a stable equilibrium state. Its displacement from the equilibrium, x(t), satisfies the simple harmonics oscillator equation:

d^2 x dt^2

  • ω^2 x = 0.

(a) What is the physical significance of the quantity ω appearing in the above equation? (b) What is the characteristic period of the oscillation? (c) Write a solution to the above equation for which x(0) = 0 and ˙x(0) = v. (d) Demonstrate that E = ˙x 2 + ω^2 x^2

does not vary in time. What is the physical significance of E?

  1. Consider a one-dimensional wave in a uniform medium. Suppose that the wave disturbance, y(x, t), satisfies the wave equation

∂^2 y ∂t^2

= v^2

∂^2 y ∂x^2

(a) What is the physical significance of the quantity v appearing in the above equation? (b) What is the dispersion relation for standing waves? Define all terms in your answer. (c) What is the dispersion relation for traveling waves? (d) Write an expression for a standing wave solution of peak amplitude A and angular frequency ω. What are the wavelength and period of the wave?

(e) Write an expression for a traveling wave solution of peak amplitude A and angular frequency ω which propagates in the minus x direction. (f) Demonstrate that ∂E ∂t

∂I

∂x

where

E =

[(

∂y ∂t

  • v^2

∂y ∂x

) 2 ]

and I = −v^2

∂y ∂x

∂y ∂t

What is the physical significance of Eq. (1)? What are the physical significances of the quantities E and I?

  1. Consider standing waves in an organ pipe of length l. Let v be the speed of sound.

(a) Suppose that one end of the pipe is closed and the other end is open. What is the frequency (in Hertz) of the standing wave with the longest wavelength? What is the frequency (in Hertz) of the standing wave with the next longest wavelength? (b) Suppose that both ends of the pipe are closed. What is the frequency (in Hertz) of the standing wave with the longest wavelength? What is the frequency (in Hertz) of the standing wave with the next longest wavelength?

  1. At sea level, and 20◦C, air has a mass density of 1.2 kg/m^3 and an average atomic weight of 28.97 atomic units. Sound waves travel through such air with a characteristic speed of 343 m/s. Estimate the minimum wavelength and maximum frequency (in Hertz) of sound waves due to the fact that air is made up of discrete atoms, rather than being a continuous fluid. The mass of a proton is 1. 67 × 10 −^27 kg.