1. After adding 2 points to everyone’s score.
PHY2053 Exam 2
Average = 11.6
High = 20 (2 students)
Low = 3
After adding 2 points to everyone’s score.
R. Field 11/12/ University of Florida
PHY 2053

2. Estimated Course Grades
18 students have 100 points!
Assumes that you get the same grade on the Final Exam that you averaged on Exam 1 plus Exam 2.
Include the first 8 quizzes and assumes that you get the same average on all your remaining quizzes that you have for the first 8 quizzes.
Includes the first 9 WebAssign HW assignments and assumes that you get the same average on all your remaining homework assignments that you have for the first 9 assignments.
Includes your HITT scores through 10/31/13 and assumes you maintain the same average on the remaining HITT questions.
Includes your first 4 Sakai HW assignments and assumes you maintain the same average on the remaining assignments.
R. Field 11/12/ University of Florida
PHY 2053

3. Traveling Waves: Energy Transport
A “wave” is a traveling disturbance that transports energy but not matter. v
Intensity:
Intensity I = power per unit area
Intensity is proportional to the square of the amplitude A!
(measured in Watts/m2)
Variation with Distance: If sound is emitted isotropically (i.e. equal intensity in all directions) from a point source with power Psource and if the mechanical energy of the wave is conserved then
(intensity from isotropic point source)
Speed of Propagation: The speed of any mechanical wave depends on both the inertial property of the medium (stores kinetic energy) and the elastic property (stores potential energy).
Transverse wave on a string:
FT = string tension
m = M/L = linear mass density
(wave speed)
R. Field 11/12/ University of Florida
PHY 2053

4. Constructing Traveling Waves
Constructing Traveling Waves: To construct a wave with shape y = f(x) at time t = 0 traveling to the right with speed v replace x by x-vt.
Traveling Harmonic Waves: Harmonic waves have the form y = A sin(kx + f) at time t = 0, where k is the "wave number“, k = 2p/l, l is the "wave length". and A is the "amplitude". To construct a harmonic wave traveling to the right with speed v, replace x by x-vt as follows:
where w = kv.
Speed of propagation!
Harmonic wave traveling to the right
Harmonic wave traveling to the left
The phase angle f determines y at x = t = 0, y(x=t=0) = Asinf. If y(x=t=0) = 0 then f = 0.
R. Field 11/12/ University of Florida
PHY 2053

5. Waves: Mathematical Description
wave traveling to the right F
Vector A with length A undergoing uniform circular motion with phase F = kx – wt. The projection onto the y-axis gives y = Asin(kx – wt).
If t = 0 then
One circular revolution corresponds to F = 2p = kl, and hence k = 2p/l (“wave number”).
R. Field 11/12/ University of Florida
PHY 2053

6. Waves: Mathematical Description
wave traveling to the right F
Vector A with length A undergoing uniform circular motion with phase F = kx – wt. The projection onto the y-axis gives y = Asin(kx – wt).
If x = 0 then
One circular revolution corresponds to F = 2p = wT and hence T = 2p/w (“period”).
R. Field 11/12/ University of Florida
PHY 2053

7. Waves: Mathematical Description
In General
wave traveling to the right F
Overall phase F = kx – wt + f.
wave traveling to the left F
Period (in s)
Frequency (in Hz)
Wave Number (in rad/m)
Wave Speed (in m/s)
Angular Frequency (in rad/s)
R. Field 11/12/ University of Florida
PHY 2053

8. Waves: Mathematical Description
wave traveling to the right
vnode x
point on string
nth node
Waves Propagation: A node is a point on the wave where y(x,t) vanishes:
(wave speed)
Transverse Speed & Acceleration: For “transverse” waves the points on the string move up and down while the wave moves to the right.
transverse speed of a point on the string
transverse acceleration of a point on the string
SHM
R. Field 11/12/ University of Florida
PHY 2053

9. Waves: Example Problems
A transverse wave on a taught string has amplitude A, wavelength l and speed v. A point on the string only moves in the transverse direction. If its maximum transverse speed is umax, what is the ratio umax/v?
Answer: 2pA/l
The function y(x,t) = Acos(kx - wt) describes a wave on a taut string with the x-axis parallel to the string. The wavelength is l = 3.14 cm and the amplitude is A = 0.1 cm. If the maximum transverse speed of any point on the string is 10 m/s, what is the speed of propagation of the travelling wave in the x-direction?
Answer: 50 m/s
R. Field 11/12/ University of Florida
PHY 2053

10. Waves: Example Problems
A sinusoidal wave moving along a string is shown twice in the figure. Crest A travels in the positive direction along the x-axis and moves a distance d = 12 cm in 3 ms. If the tick marks along the x-axis are 10 cm apart, what is the frequency of the traveling wave?
Answer: 100 Hz
R. Field 11/12/ University of Florida
PHY 2053