Describing Waves

traveling disturbances

§ 14.1–14.2

What’s a Wave?

• Oscillation– object moves cyclically

• Wave– medium moves cyclically– disturbance travels, medium does not

Group Whiteboard Work

2. A wave generator produces 10 pulses each second. The pulses travel at 300 cm/s.

a. What is the period of the waves?

b. What is the wavelength of the waves?

Wave Pulse

• Why does the pulse move?

• What determines its speed?

• What happens inside the medium?

Points to Ponder

The particles of the string change their motion as the wave travels. What force accelerates them?

a cb

d

What are the velocity and acceleration of the string particles at the following positions? Why?

a. middle (leading edge)b. crest

c. middle (trailing edge)d. trough

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

Wave Speed

• Speed of disturbance traveling through the medium

• Generally not the speed of the oscillating medium itself!

Periodic Waves

repeat in time and space

§ 15.2

• Wavelength: crest-crest distance• Trough: low point

• Period: crest-crest-timing

Features of a Wave

• Crest: high point

crest

trough

Periodic Wave Parameters

• Angular frequency = (rad/s)

• Cycle frequency f = /2 (cycle/s)

• Repeat time = period T = 1/f (s/cycle)

• Repeat distance = wavelength (m/cycle)

• Angular wavenumber k = 2/ (rad/m)

• Wave speed v = /T = f = /k (m/s)

Poll Question

Doubling the frequency of a wave while keeping its speed constant will cause its wavelength to

A. increase.B. decrease.C. stay the same.

Poll Question

Doubling the frequency of a wave while keeping its wavelength constant will cause its speed to

A. increase.B. decrease.C. stay the same.

Poll Question

Doubling the wavelength of a wave while keeping its speed constant will cause its period to

A. increase.B. decrease.C. stay the same.

Propagation Speed

in a rope

§ 14.2

Purely transverse wave

In a rope, string, or spring:

•Speed increases with tension F

•Speed decreases with density

v =     F/

Wave Functions

oscillations extended

§ 14.3

Think Question

• The waves travel to the right.

In which direction is A moving right now?A. A is momentarily stationary.

B. Upward. C. Downward.

A B

• A and B are points on the medium.

CD

Poll Question

• The waves travel to the right. • A and B are points on the medium.

In which direction is B moving right now?A. B is momentarily stationary.

B. Upward. C. Downward.

A B

CD

Think Question

• The waves travel to the right. • A and B are points on the medium.

In which direction is C moving right now?A. C is momentarily stationary.

B. Upward. C. Downward.

A B

CD

Think Question

• The waves travel to the right. • A and B are points on the medium.

In which direction is D moving right now?A. D is momentarily stationary.

B. Upward. C. Downward.

A B

CD

Formula Description

Displacements y of A and B with time

A B

y(xA,t) = A cos(t)

y(xA+/4,t) = A cos(t–2/4)

yA yB

ty

+A

−A

generalize to any x

Formula Description

y(xA,t) = A cos(t)

y(xA+/4,t) = A cos(t–2/4)

y(x,t) = A cos(t–kx)

same as

y(x,t) = A cos(kx–t)

where

–k(/4) = –2/4

k = 2/

Parameters

= 2/T = angular frequency (rad/s)

k = 2/ = wave number (rad/m)

Graphing y (x,t)

Each tells only part of the story!

y(x = 0)

y(t = 0)

x

t

T

snapshot of the wave at one time

displacement of the medium at one place

3D Graph

x

t

cresttrough

T

slope = v

Displacement-position-time

Traveling the Other Way

x

t

cresttrough

T

slope = v

Displacement-position-time