1. Whiteboard Work
A child on a playground swing makes a complete to-and-fro swing every 2 seconds.
What is the frequency of the swinging?
What is the period of the swinging?
For this lecture, have the following supplies &c:
Demo equipment: table clamp, long coil spring, ropes of different weights, long slinky
Websites: Dan Russel’s wave types animations, Northwestern’s Wave Superposition2 applet
Sound files: beats
Don’t forget the units!

2. Waves
Part 1: Basics

3. Objectives Identify the parts of a wave.
Relate wave speed, frequency, wavelength, and period.
Trace the movement of the medium in a string wave, in a sound wave, and in a compression wave in a spring.

4. What’s the Point?
How are waves described?
Why do waves occur?

5. Week Outline Waves in One Dimension Combinations of Waves
Features of Waves
Types of Waves
Combinations of Waves
Interference
Standing Waves

6. Waves and Vibrations Vibrations: Repeat in time
no net displacement of disturbance
no net displacement of medium
Waves: Repeat in time and space
wave travels

7. Features of a Wave crest trough Crest: high point Trough: low point
Wavelength: crest-crest distance
crest
Period: crest-crest-timing
Here we define names for wave features so that we can communicate easily. l
trough

8. Features of a Wave Amplitude A: (crest height – trough height) / 2
Frequency f: repeats in a given time (= 1/T)
Velocity u: speed of crest motion
Here we define names for wave features so that we can communicate easily. u A

9. Relations between Features
Period T = 1 / f ; Frequency f = 1 / T
Velocity u = l / T
= lf
Wavelength l = uT = u / f
Frequency f = u / l; Period T = l / u

10. Group Question
Doubling the frequency of a wave while keeping its speed constant will cause its wavelength to
increase.
decrease.
stay the same.

11. Group Question
Doubling the speed of a wave while keeping its wavelength constant will cause its frequency to
increase.
decrease.
stay the same.

12. Group Question
Doubling the wavelength of a wave while keeping its frequency constant will cause its speed to
increase.
decrease.
stay the same.

13. Group Whiteboard Work
A wave generator produces 10 pulses each second. The pulses travel at 300 cm/s.
What is the period of the waves?
What is the wavelength of the waves?

14. Wave Pulse in a Rope Why does the pulse move?
What determines its speed?
What is happening inside the rope?
Model: a chain of students holding hands, half-crouched. Tell them that the connections between them are like springs under tension and that their motions follow Newton’s Laws. Review: force proportional to spring displacement, acceleration follows force and mass, spring applies opposite force to segments on opposite ends.

15. Prediction
Increasing the tension on a rope will make waves travel along the rope
faster.
slower.
At the same speed (no effect).
Demonstrate with coil spring or rope increasing tension. Rope is less ambiguous because its length density does not change appreciably with tension.

16. Prediction
Increasing the length density (mass per meter) of a rope will make waves travel along the rope
faster.
slower.
At the same speed (no effect).
Demonstrate with two different ropes. They need to be fairly long.

17. Points to Ponder a c b d
What are the velocity and acceleration of the string particles at the following positions? Why?
middle (leading edge)
crest
middle (trailing edge)
trough
The particles of the string change their motion as the wave travels. What force accelerates them?
Tension yields a net force where rope is curved.
a is moving downward with momentarily zero acceleration
b is momentarily motionless with downward acceleration
c is moving upward with momentarily zero acceleration
d is momentarily motionless with upward acceleration

18. Types of Waves
Motion of the medium is perpendicular to the direction the wave travels: transverse wave (example: string wave)
Motion of the medium is parallel to the direction the wave travels: longitudinal wave (examples: sound wave, slinky wave)
Animation
Crest and trough of a longitudinal wave: moving regions of highest and lowest pressure or density. Amplitude of a longitudinal wave: Half the total change in pressure or density

19. Question “The Wave” performed by sports fans is an example of
a longitudinal wave.
a transverse wave.
an unnatural wave.
Class activity: make a longitudinal audience wave

20. Combining Waves

21. Group Work
Sketch the wave resulting from the addition of the two waves shown at one instant. 3 –3

22. Group Work
Sketch the wave resulting from the addition of the two waves shown at one instant. 3
result –3

23. Interference Constructive: Sum of waves has increased amplitude
Destructive: Sum of waves has decreased amplitude
Two-wave simulation
Run at: w1 = 0.2; k1 = 0.2; ampl = 15
integral multiples (half, third, quarter) of lambda: multiply W1, k1 by 2, 3, 4
add same-lambda wave with negative amplitude
Beats: slightly vary w2 and k2 together from wave 1 values (0.22 and 0.22; 0.21 and 0.21, etc.)
Standing waves (use w of about 0.2; try w = 0.2, k = 0.1)

24. Beats
Waves of similar frequency combine to give alternating times of constructive and destructive interference
Distinctive “waa-waa” sound with beat frequency equal to the difference in frequency of the component waves (Why?)
(sound files)