Workshop Overview Waves 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.
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 interactive stopwatch This onscreen stopwatch makes the application activity more fun!
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
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
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 NameFrequencyC majorC minorD 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 NameFrequencyC majorC minorD 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 528Optional Tuning Notes for Chords
Note NameFrequencyC majorC minorD major C 264 Yes D flat 285 D 297 E flat 317 Yes E 330 Yes F 352 G flat 380 G 396 Yes A flat 422 A 440 B flat 475 B 495 C 528Optional Tuning Notes for Chords
Note NameFrequencyC majorC minorD major C 264 Yes D flat 285 D 297 Yes E flat 317 Yes E 330 Yes F 352 G flat 380 Yes G 396 Yes A flat 422 A 440 Yes B flat 475 B 495 C 528Optional 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 9/85/44/33/25/315/8 2 DOREMIFASOLA TI TIDO 264297330352396440495528 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 Frequency of Middle C
Sound and Music - Beats Small Difference in Frequency Product of Interference
Palm Pipes Check to see the note of your palm pipe Follow along with the music and play your palm pipe when your note occurs. How could pipes that have the same note be different lengths? Can you tell what key each song is in?
Note Name Key ColorFrequency 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.