Chapter 25

Vibrations and Waves

Vibration – a wiggle in time

For example: moving back and forth in the same space, ie., pendulum.

**A vibration exists over time.**

Wave – a wiggle in space andand time

For example: light and sound

**A wave exists over space and time**

25.1 Vibration of a Pendulum

•Pendulums swing “to and fro” (back and forth)

•The time of the “to and fro” is called a period.

Periods

•Periods depend only on 2 things:–The length of the pendulum and

–The acceleration of gravity

Periods•T = period

L= the length of the pendulum g = acceleration of gravity = “pi” 3.14…

T = 2 L/g

Periods

The longer the pendulum, the

greater the period.

25.2 Wave Description

•The back and forth motion of the pendulum (aka “oscillatory motion”) is called simple harmonic motion.

Simple Harmonic Motion

In simple harmonic motion…

the restoring force is proportional to the displacement from equilibrium.

Major parts of a wave:Midpoint (Equilibrium)

Crests and Troughs

Crest (high point)

Trough (low point)

Amplitude - distance from midpoint to crest or trough

Wavelength () – distance from one crest (trough) to the next

Frequency (f)how frequently a vibration occurs

(# of crests per second)vibrations per second

Heinrich HertzHeinrich Hertz demonstrated

radio waves in 1886.The unit of frequency is the

Hertz.1 vibration per second = 1 Hertz

Kilohertz = 1000 v/secMegahertz = 1000000 v/sec

Frequency and Period

•Frequency and period are reciprocals of each other.

•Frequency = 1 period•Period = 1 frequency

What is the frequency in v/sec of a 100-hertz wave?

•Answer:a 100 hertz wave vibrates 100 times in 1 second.

What is the period of vibration of a 100-hertz wave?•Answer:period = 1/frequencyperiod = 1/100each period is 1/100 of a second

25.3 Wave Motion

Sound and light waves move.

As waves move, matter is NOT passed along them.

For example:When you create a

wave with a rope, it is the disturbance that

moves along the rope, not the rope itself.

25.4 Wave Speed

How fast a wave moves depends on the

medium of the wave.

Wave speed is related to the frequency and wavelength of the wave.

v = fWave speed (m/s) =

frequency (Hz) X wavelength (m)

Example:What is the speed of a wave with a frequency

of 100 Hz and a wavelength of .025

meters?

Answer:v = fλ

Speed = 100 Hz X .025 m

Speed = 2.5 m/s

25.5 Transverse Waves

Waves produced when the motion of the medium is at right angles to the direction in which the wave travels.EX: a fishing bobber in a

lake

25.6 Longitudinal Waves

Waves produced when the particles move

ALONG the direction of the wave rather than at right angles to itEX: Sound waves

25.7 Interferenceoverlapping waves

Interference pattern: patterns formed when waves overlap

2 types of interference:1.constructive –

reinforcing interference when waves align at the crests and troughs**individual effects are

increased**

Constructive Interference

2.Destructive – cancellation interferencewhen the crest of one wave aligns with the trough of another**their individual effects are reduced**

Destructive Interference

25.8 Standing WavesCaused by interference

Standing WavesIncident wave – initial wave

Reflected wave – wave that reflects back from interference

When aligned, incident and reflected waves form

a standing wave

NODESIn a standing wave,

parts of the rope remain stationary.

These parts are called nodes.

ANTINODESPoints along a wave that occur half way between

nodes.Antinodes are the points

that have the largest amplitude.

Antinodes become the crests & troughs.

NODES and ANTINODES

The Doppler Effect•Christian Doppler (1803-1853)

•Change in frequency due to the motion of a sound source

The Doppler EffectBlue shift = frequency increases as it approachesRed shift = frequency decreases as it leaves

Blue Shift Red Shift

Higher frequency Lower frequency

Galaxies show a red shift in the light they emit.

Bow wavesEX: swimming faster than

the waves you’re producing

Shock waves – 3-dimensional bow wavesEX: a speed boat moves much faster than the waves it produces

SONIC BOOM – the sharp crack heard when the shock wave that sweeps behind a supersonic aircraft reaches the listener.

A slower aircraft sends sound wave crests one at a time and we hear it as a continuous noise.

FORMULAS FOR CHAPTER 25:

T = 2 L/gFrequency = 1/periodPeriod = 1/frequency

v = f