Chapter 12: Vibrations and Waves

Section 1: Simple harmonic motionSection 2: Measuring simple harmonic motionSection 3: Properties of wavesSection 4: Wave interactions

Simple harmonic motion Simple harmonic

motion – vibration about an equilibrium position in which a restoring force is proportional to the displacement from equilibrium.

Simple harmonic motion

Simple harmonic motion Hooke’s Law

Felastic= -kx

Two examples Mass on a spring Pendulum

Simple harmonic motion

Measuring simple harmonic motion Amplitude: the

maximum displacement from equilibrium.

Period (T): the time it takes to execute a complete cycle of motion.

Frequency (f): the number of cycles of vibration per unit time. f = 1/T or T = 1/f f = 1/T = 1/20s =

0.05Hz

Measuring simple harmonic motion

Calculating the Period Simple Pendulum

Calculating the Period Mass on a spring

g

LT 2

k

mT 2

Properties of waves Two main classifications of waves

Electromagnetic (will study later) Visible light, radio waves, microwaves, and

X rays No medium required

Mechanical (will study now): a wave that propagates through a deformable, elastic medium Must have a medium Medium: the material through which a

disturbance travels

Properties of waves Wave Types

Pulse wave: a single, nonperiodic disturbance

Periodic wave: a wave whose source is some form of periodic motion Usually simple

harmonic motion Sine waves describe

particles vibrating with simple harmonic motion

Properties of waves Parts of a wave

Crest The highest point

above the equilibrium position

Trough The lowest point

below the equilibrium Wavelength

The distance between two adjacent similar points of the wave, such as crest to crest.

Properties of waves Transverse

A wave whose particles vibrate perpendicularly to the direction of wave motion

Examples include: water waves and waves on a string

Longitudinal A wave whose particles

vibrate parallel to the direction of wave motion

Sometimes called compression waves

Examples include: sound waves, earthquakes, electromagnetic waves

Properties of waves Wave speed

λ is wavelength For all

electromagnetic waves v = 3.00x108 m/s

For sound waves v = 340 m/s

(approximately)

fv

Wave interactions

Wave interference Constructive interference

Interference in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave.

Add the two amplitudes to get total amplitude of two new waves

Wave interactions

Wave interference Destructive interference

Interference in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave

Again add the two amplitudes together. The wave on bottom should be negative however.

Wave interference compare

Wave interactions Reflection

Depends on the boundary

Wave interactions Standing waves (the wave will appear to be standing still)

A wave pattern that results when two waves of the same frequency, wavelength, and amplitude travel in opposite directions and interfere

Node A point in a standing wave that always undergoes complete destructive

interference and therefore is stationary Antinode

A point in a standing wave, halfway between two nodes, at which the largest amplitude occurs.

Wave interactions Standing waves calculations

Must be a node at each end of the string In letter (b) we see that

this is ½ a wavelength. Thus for the first standing

wave, the wavelength equals 2L

In letter (c) we see a complete wavelength. Thus for the second

standing wave, the wavelength equals L

In letter (d) we see 1½ or 3/2 of a wavelength Thus for the third standing

wave, the wavelength equals 2/3 L

Wave interactions

Practice problem 1 A wave with an amplitude of 1 m

interferes with a wave with an amplitude of 0.8 m. What is the largest resultant displacement that may occur?

Wave interactions

Practice problem 2 A 5 m long string is stretched and fixed

at both ends. What are three wavelengths that will produce standing waves on this string?

Wave interactions

Practice problem 3 A wave with an amplitude of 4 m

interferes with a wave with an amplitude of 4.1 m. What will be the resulting amplitude if the interference is destructive? If the interference is constructive?