waves. chapter twenty-three: waves 23.1 harmonic motion 23.2 properties of waves 23.3 wave motion

WAVES

Chapter Twenty-Three: Waves

23.1 Harmonic Motion

23.2 Properties of Waves

23.3 Wave Motion

Chapter 23.1 Learning Goals

Identify examples of simple oscillators.

Compare and contrast harmonic motion with linear and curved motion.

Apply a rule to determine the frequency and period of an oscillator.

Investigation 23A

Key Question:How do we describe the

back and forth motion of a pendulum?

Harmonic Motion

23.1 Harmonic motion

A. Linear motion gets us from one place to another.

B. Harmonic motion is motion that repeats over and over.

23.1 Harmonic motionA pendulum is a device that swings back and force.

A cycle is one unit of harmonic motion.

23.1 Oscillators

An oscillator is a physical system that has repeating cycles or harmonic motion.

Systems that oscillate move back and forth around a center or equilibrium position.

23.1 OscillatorsA restoring force is any force that always acts to pull a system back toward equilibrium.

23.1 Harmonic motionHarmonic motion can be fast or slow, but speed constantly changes during its cycle.

We use period and frequency to describe how quickly cycles repeat themselves.

The time for one cycle to occur is called a period.

23.1 Harmonic motionThe frequency is the number of complete cycles per second.

Frequency and period are inversely related.

One cycle per second is called a hertz, abbreviated (Hz).

Solving Problems

The period of an oscillator is 2 minutes.

What is the frequency of this oscillator in hertz?

1. Looking for: …frequency in hertz

2. Given …period = 2 min

3. Relationships: …60 s = 1 min … f = 1/T

4. Solution … f = 1/120 s

Solving Problems

f = .008 Hz

23.1 AmplitudeAmplitude describes the “size” of a cycle.

The amplitude is the maximum distance the oscillator moves away from its equilibrium position.

23.1 AmplitudeThe amplitude of a water wave is found

by measuring the distance between the highest and lowest points on the wave.

The amplitude is half this distance.

23.1 Amplitude

A pendulum with an amplitude of 20 degrees swings 20 degrees away from the center in either direction.

23.1 DampingFriction slows a pendulum down, just as it slows all motion.

Damping is the gradual loss of amplitude.

23.1 Graphs of harmonic motionA graph is a

good way to show harmonic motion because you can quickly recognize cycles.

Graphs of linear motion do not show cycles.

23.1 Natural frequency and resonance

The natural frequency is the frequency (or period) at which a system naturally oscillates.

Every system that oscillates has a natural frequency.

23.1 Natural frequency and resonance

You can get a swing moving by pushing it at the right time every cycle.

A force that is repeated over and over is called a periodic force.

23.1 Natural frequency and resonance

Resonance happens when a periodic force has the same frequency as the natural frequency.

When each push adds to the next one, the amplitude of the motion grows.

Chapter Twenty-Three: Waves

23.1 Harmonic Motion

23.2 Properties of Waves

23.3 Wave Motion

Chapter 23.2 Learning Goals

Describe the properties and behavior of waves.

Calculate the speed of waves.

Identify the parts of a wave.

Investigation 23B

Key Question: What is resonance and why is it

important?

Natural Frequency and Resonance

23.2 WavesA wave is an oscillation that travels

from one place to another.

If you poke a floating ball, it oscillates up and down.

The oscillation spreads outward from where it started.

23.2 WavesWhen you drop a ball into water, some of the water is pushed aside and raised by the ball.

23.2 WavesWaves are a traveling form of energy because they can change motion.

Waves also carry information, such as sound, pictures, or even numbers.

23.2 Frequency, amplitude, and wavelength

You can think of a wave as a moving series of high points and low points.

A crest is the high point of the wave.

A trough is the low point.

23.2 Frequency

The frequency of a wave is the rate at which every point on the wave moves up and down.

Frequency means “how often”.

23.2 Amplitude

The amplitude of a water wave is the maximum height the wave rises above the level surface.

23.2 WavelengthWavelength is the distance from any

point on a wave to the same point on the next cycle of the wave.

The distance between one crest and the next crest is a wavelength.

23.2 The speed of wavesThe speed of a water wave is how fast

the wave spreads, NOT how fast the water surface moves up and down or how fast the dropped ball moves in the water.

How do we measure the wave speed?

23.2 The speed of wavesA wave moves one

wavelength in each cycle.

Since a cycle takes one period, the speed of the wave is the wavelength divided by the period.

23.2 The speed of wavesThe speed is the distance traveled

(one wavelength) divided by the time it takes (one period).

We usually calculate the speed of a wave by multiplying wavelength by frequency.

Solving Problems

The wavelength of a wave on a string is 1 meter and its speed is 5 m/s.

Calculate the frequency and the period of the wave.

1. Looking for: …frequency in hertz …period in seconds

2. Given … = 1 m; s = 5 m/s

3. Relationships: s = f x or f = s ÷ f = 1/T or T = 1/f

4. Solution f = 5 m/s ÷1 m = 5 cycles/s T = 1/5 cycles/s = .2 s

Solving Problems

f = 5 Hz

T = .2 s

Chapter Twenty-Three: Waves

23.1 Harmonic Motion

23.2 Properties of Waves

23.3 Wave Motion

Chapter 23.3 Learning Goals

Distinguish between transverse and longitudinal waves.

Demonstrate an understanding of wave interactions.

Distinguish between constructive and destructive interference.

23.3 Wave MotionA wave front is the

leading edge of a moving wave which is considered to be the crest for purposes of modeling.

The crests of a plane wave look like parallel lines.

The crests of a circular wave are circles.

23.3 Four wave interactions When a wave

encounters a surface, four interactions can occur:

1. reflection,

2. refraction,

3. diffraction, or

4. absorption.

23.3 Wave interactionsA boundary is an edge or surface where things change.

Reflection, refraction, and diffraction usually occur at boundaries.

23.3 Wave interactions

Diffraction usually changes the direction and shape of the wave.

When a plane wave passes through a small hole diffraction turns it into a circular wave.

23.3 Transverse and longitudinal waves

A wave pulse is a short ‘burst’ of a traveling wave.

It is sometimes easier to see the motion of wave pulses than it is to see long waves with many oscillations.

23.3 Transverse waves

The oscillations of a transverse wave are not in the direction the wave moves.

23.3 Longitudinal wavesThe oscillations of a longitudinal wave are in the same direction that the wave moves.

23.3 Constructive interferenceConstructive interference happens when

waves add up to make a larger amplitude.

Suppose you make two wave pulses on a stretched string.

One comes from the left and the other comes from the right.

When the waves meet, they combine to make a single large pulse.

23.3 Destructive interferenceWhat happens when one pulse is on

top of the string and the other is on the bottom?

When the pulses meet in the middle, they cancel each other out.

During destructive interference, waves add up to make a wave with smaller or zero amplitude.

Investigation 23C

Key Question:How do waves move?

Waves in Motion

Cell Phones: How they workThe process that allows a cell phone to

communicate is the same as for a radio or walkie-talkie. All of these devices use electromagnetic waves of within a specific frequency range to send information.