Sound and WavesUnit 4

Workshop OverviewWaves and Sound: Unit 4

Inv. 11.1: Harmonic Motion (pendulum)

Inv. 12.2: Waves in Motion (wave tray)

Inv. 12.3: Natural Frequency and Resonance (waves on a string)

Selected parts of investigations in Chapter 13 – Sound.

Investigation 11.1 Harmonic Motion

Harmonic MotionMotion that repeats itself over and over

Examples of harmonic motion

Rotation and revolution of Earth

Back and forth motion of a swing

Turning bicycle wheel

OscillatorObjects or systems that exhibit harmonic

motion

Examples of oscillators

Earth

Vibrating guitar string or tuning fork

Quartz crystal timekeeper in watch or computer

Pendulum!

Pendulum

Excellent device for learning about oscillators and harmonic motion

Apply basic pendulum concepts to more sophisticated behavior, such as waves and sound.

Four New Ideas

Speed, velocity, and acceleration are great ways to describe linear motion, but not harmonic motion.

Need 4 new ideas: Cycle Period Frequency amplitude

Experimenting with the Pendulum:Investigation 11.1

Set up the pendulum

Setting up the Photogate

Using the Timer with the Pendulum

IMPORTANT INFO

When you use the timer in period mode, the period represents the time between breaks of the photogate beam. Therefore, since the pendulum bob breaks the beam twice in one complete cycle, you need to multiply the reading on the timer by TWO to get the time for one cycle (period).

MORE IMPORTANT INFO

The “reset” button works differently in period mode. When you hit reset once, it freezes the display. Hit reset again, and you will reset the display.

After a reset, you must let the bob swing through the photogate at least twice before another reading will show up on the timer.

Let’s investigate!

Watch the pendulum swing through the photogate. Play with this awhile until you get the bob to swing through without hitting the gate. Use leveling feet to level your stand Pull string out to the end of the slot so the

bob doesn’t hit the pole

Cycle: smallest complete unit of motion that repeats.

Period: the time it takes to compete one cycle

Amplitude: maximum displacement the oscillator moves away from average or resting position

Frequency: number of cycles an oscillator completes per unit of time (cycles per sec).

About the pendulum…

Demonstrate one complete CYCLE of the pendulum.

How will you measure the PERIOD of the pendulum? (Period is more useful than frequency when studying slow oscillators).

How will you measure the AMPLITUDE of the pendulum?

What variables affect the period of the pendulum?

You can change 3 variables of a pendulum: Mass Amplitude String length

Devise a controlled experiment (or a series of mini experiments) to determine which variables significantly affect the period. Change each variable by a large amount; 3 trials is sufficient.

Hints

Changing mass: use the cord stop to hold washers on the string behind the pendulum face:

Measure from top of string to bottom of washers

Which variable significantly affects the period of the

pendulum?

String Length

Application

Make a 30-sec clock, accurate to within 0.5 seconds!

interactive stopwatch This onscreen stopwatch makes the application

activity more fun!

Investigation 12.2 Waves in Motion

Bridging the Concepts

Waves are oscillations that TRAVEL; a pendulum stays in one place.

Waves carry oscillations from one place to another

Waves carry information from one place to another!

How do waves move and interact?

Fill tray with about 1 cm of colored water

Practice making transverse waves by using plastic wand

Practice making circular waves by dipping your finger in the water

How do waves interact with boundaries and materials?

Diffraction: how waves change shape when passing through openings or around obstacles

Model how diffraction can occur in the wave tray

Examples of diffraction Hearing someone through a crack in a door Diffraction grating glasses

How do waves interact with boundaries and materials?

Reflection: how waves bounce off of things

Model how reflection can occur in the wave tray

Examples of reflection: Echo Seeing yourself in a mirror

How do waves interact with boundaries and materials?

Refraction: how waves can be bent when they pass through a boundary

refraction will be modeled in the unit on light

Examples of refraction: Eyeglasses telescopes

Investigation 12.3 Natural Frequency

and Resonance

Bridging the Concepts

Waves usually travel, but you can make a wave stay in one place to study it.

Standing Wave: wave trapped in one spot

To make standing waves, you need boundaries to bounce or reflect the wave back on itself Sound: boundaries are hard surfaces Light: boundaries could be mirrors

Standing Waves in Daily Life

Flute: standing wave of sound inside the instrument

Wave pool: standing wave of water

Laser: standing wave of light

Guitar string: standing wave on a vibrating string

Standing Wave on a String

We can make standing waves and study them by using the CPO wave generator equipment

Basic characteristics of waves

Frequency “how often” (cycles/sec,

wiggles/sec, ) Hertz

Wavelength Length of one wave (“S” shape)

Basic characteristics of waves

Node Points where the string

does not move

Anti-node Points where the string

moves the most

Common Uses for Waves

Radio waves are used to carry signals over large distances

Ultrasound uses very high frequency sound waves to make images of the inside of the body

Light is a wave that has different frequencies we call colors

Set up a Wave Experiment

Change The Frequency

Observe the string as you change the frequency

Describe What Happens

Patterns on the String

Standing Wave Patterns

OBSERVATONS

The string vibrates

Standing Wave patterns appear at some frequencies

All of these frequencies are multiples of the lowest one that produces this effect

The frequency multiplied by the wavelength of each standing wave is the same for all of the waves

Other things to try

Measure the amplitude at different frequencies

Measure the frequency at which a certain harmonic occurs for different string tensions

RESONANCE A Condition where a Driving Force or push

occurs at a frequency that results in a Standing Wave

These Standing Waves occur at what are called Natural Frequencies or Harmonics

Every object, substance and material has its own Natural Frequencies, where they “like” to vibrate

All Natural Frequencies are multiples of the Fundamental

FREQUENCY x WAVELENGTH Each Harmonic has a different frequency

and wavelength

Frequency x Wavelength gives the same answer for ALL Harmonics

Cycles/Seconds x Meters/Cycle= Meters/Second which is a value for speed of the Wave on the string

If Frequency increases, Wavelength decreases and if Frequency decreases, Wavelength increases

Chapter 13 investigation overview

Sound Waves

How do we perceive Sound Waves?

What do they have in common with other kinds of waves?

What is different about Sound Waves?

Set Up a Sound Experiment Disconnect the Wiggler from the Sound and

Waves Machine

Connect Mini-Speakers to the Sound and Waves Machine

Switch the CPO Timer II to Sound Mode

Note Name Frequency C major C minor D major

C 264

D flat 285

D 297

E flat 317

E 330

F 352

G flat 380

G 396

A flat 422

A 440

B flat 475

B 495

C 528

Tuning Notes for Chords

Note Name Frequency C major C minor D major

C 264 Yes

D flat 285

D 297

E flat 317

E 330 Yes

F 352

G flat 380

G 396 Yes

A flat 422

A 440

B flat 475

B 495

C 528 Optional

Tuning Notes for Chords

Note Name Frequency C major C minor D major

C 264 Yes Yes

D flat 285

D 297

E flat 317 Yes

E 330 Yes

F 352

G flat 380

G 396 Yes Yes

A flat 422

A 440

B flat 475

B 495

C 528 Optional Optional

Tuning Notes for Chords

Note Name Frequency C major C minor D major

C 264 Yes Yes

D flat 285

D 297 Yes

E flat 317 Yes

E 330 Yes

F 352

G flat 380 Yes

G 396 Yes Yes

A flat 422

A 440 Yes

B flat 475

B 495

C 528 Optional Optional

Tuning Notes for Chords

Sound and Music - Chords

Different notes have different frequencies

Chords are combinations of different notes with specific mathematical relationships

Different relationships of the notes will produce chords with very different “moods” or “feel”

The Musical Scale Mathematical Relationships in the form of

Ratios

1 9/8 5/4 4/3 3/2 5/3 15/8 2

DODO RERE MIMI FAFA SOSO LALA TITI DODO

264 297 330 352 396 440 495 528

C D E F G A B C

Different frequencies for Middle C

Click on the link below for a brief discussion of why the frequency of middle C can differ.

Frequency of Middle C

Sound and Music - Beats Small Difference in Frequency

Product of Interference

Note Name Key Color Frequency

C 528

B 495

B flat 475

A 440

A flat 422

G 396

G flat 380

F 352

E 330

E flat 317

D 297

D flat 285

C 264

Musical Instruments Musical instruments play different

notes

Frequencies are controlled by altering wavelength

Vibrating materials like strings or reeds cause chunks or columns of air to vibrate

Musical Instruments

Natural Frequencies/Harmonics cause amplification through Resonance

Instruments can be amplified this way and/or electronically

The vibrating element vibrates at ALL its Harmonics, not just the Fundamental.

The combination of these frequencies give an instrument its particular sound.

Questions/Answers