Waves Notes

WAVES

WAVE MOTION

Observational Experiment 1: Water

• Drop a rock in water and observe the resulting waves.
• Consider the observations and propose explanations for what happens after the rock hits the water.

Testing Experiment 1

• Drop a rock in water with lilypads floating nearby.
  • Predictions: Make predictions about what will happen to the lilypads.
  • Outcome: Record the actual outcome of the experiment.
  • Judgement: Judge whether the predictions matched the outcome.

What Is Moving?

• The water itself is not moving outwards; instead, the parts of the water interact with adjacent parts, causing them to move up and down.
• Each individual piece of water vibrates up and down.
• Only energy is moving outwards.
• Matter (the water particles) is only vibrating due to interactions with adjacent particles.

Observational Experiment 2: Slinky, One Disturbance

• Stretch out a Slinky.
• Flick one end of the Slinky quickly once.
  • Sketch the situation.
  • Record observations in words.

Observational Experiment 3: Slinky, Continuous Disturbances

• Stretch out a Slinky.
• Flick one end of the Slinky continuously.
  • Sketch the situation.
  • Record observations in words.

WAVE MOTION

• Wave motion involves disturbances produced by a vibrating object (a source).
• The disturbances propagate through a medium, causing points in the medium to vibrate.
• The moving disturbance is called a wavefront.
• A singular disturbance is called a pulse.

2 Necessary Components for Wave Motion

• Source:
  • The object that causes the disturbance (e.g., rock, person).
• Medium:
  • The substance through which the disturbance travels (e.g., water, Slinky, solid, liquid, or gas).

Energy, NOT matter

• When a source causes a disturbance in a medium, energy travels across the medium.
• The parts of the medium, like water particles, only vibrate and do not move across the medium.
• Energy moves in a wave.

Observational Experiment: Slinky, Changing One Thing

• Create consistent wave motion in a Slinky by continuously flicking one end.
• Change one aspect of the situation and observe the effect.
  • Sketch the situation before and after the change.
  • Record observations in words.

WAVE PROPERTIES

• Period (T):
  • The time interval for one complete vibration of a point in the medium.
  • Units: seconds
• Frequency (f):
  • The number of vibrations per second of a point in the medium.
  • Units: Hertz (Hz) or 1/seconds
• Speed (v):
  • The distance a disturbance travels during a time interval, divided by that time interval.
  • Units: meters per second (m/s)
• Amplitude (A):
  • The maximum distance of a point in the medium from its equilibrium position.
    • Units are meters.
  • Equilibrium position: The position of a vibrating object when not disturbed.
  • Crest: Point of Positive Amplitude.
  • Trough: Point of Negative Amplitude.
• Wavelength ($\lambda$):
  • The distance between two nearest points on a wave that have the same displacement and shape.
  • The distance between two consecutive wavefronts.
  • Units: meters

Different Types of Waves

• Transverse:
  • The disturbance is perpendicular (at a right angle) to the propagation of the wavefront.
• Longitudinal:
  • The disturbance is in the parallel (same) direction as the propagation of the wavefront.

Testing Experiment 2: Wave Motion

• Place a piece of paper on a Slinky and create continuous disturbances.
  • Prediction: Predict what will happen to the paper.
  • Outcome: Record the actual outcome.
  • Judgement: Judge whether the prediction matched the outcome.

Application Experiment 1: Water Balloon Burst!

• Apply wave motion concepts to suggest ways to improve the chances of popping a water balloon.
• Use relevant vocabulary to explain the suggestions.

WAVES: THE WAVE EQUATION

Simulation: Waves on a String

• Use the following simulation for experiments: https://phet.colorado.edu/sims/html/wave-on-a-string/latest/wave-on-a-string_en.html

Observational Experiment 1: How Tension Affects Speed

• Tension is related to the force exerted on the ends of an object.
• Use the simulation to send pulses through a string at different tensions (low to high).
  *Settings: “Pulse” in Top-Left, “No End” in Top-Right, Set Damping to “None”
• Determine the speed of a wavefront at each tension.

Outcome

• Record the tension, distance traveled, time taken, and speed for each trial.

Pattern for How Tension Affects Speed

• Hypothesis:
  • As tension increases, speed increases.
  • This is a direct relationship.

Observational Experiment 2: How Frequency Affects Wavelength

• Use the simulation to oscillate a string at different frequencies.
  *Settings: “Oscillate” in Top-Left, “No End” in Top-Right, Set Damping to “None”
• Measure the wavelength for each frequency.

Outcome

• Record the frequency and wavelength for each trial.

Pattern for How Frequency Affects Wavelength

• Hypothesis:
  • As frequency increases, wavelength decreases.
  • This is an inverse relationship.

Observational Experiment 3: How Speed Affects Wavelength

• Use the simulation to send disturbances through a string at different speeds (NOT frequencies).
  *Settings: “Oscillate” in Top-Left, “No End” in Top-Right, Set Damping to “None”
• Measure the wavelength for each speed.

Outcome

• Record the tension, speed, and wavelength for each trial.

Pattern for How Speed Affects Wavelength

• Hypothesis:
  • As speed increases, wavelength increases.
  • This is a direct relationship.

3 PATTERNS

1. As frequency increases, wavelength decreases.
2. As tension increases, speed increases.
3. As speed increases, wavelength increases.

Observational Experiment 3: How Amplitude Affects Wavelength

• Use a simulation to oscillate (vibrate) a string at different amplitudes.
  *Settings: “Oscillate” in Top-Left, “No End” in Top-Right, Set Damping to “None”
• Measure the wavelength for different amplitudes.

Outcome

• Record Amplitude vs Wavelength.

Pattern for how Amplitude affects Wavelength

• As the Amplitude changes, the Wavelength does not change.
• No Relationship!

Testing Experiment 1: How Frequency Affects Wavelength

• Use equipment to test the relationship between frequency and wavelength.
  • Hypothesis: State the hypothesis.
  • Experiment: Describe the experiment.
  • Prediction: Predict the outcome
  • Outcome: Record the actual outcome.
  • Judgement: Judge whether the prediction matched the outcome.

Testing Experiment 2: How Tension Affects Speed

• Use equipment to test the relationship between tension and speed.
  • Hypothesis: State the hypothesis.
  • Experiment: Describe the experiment.
  • Prediction: Predict the outcome
  • Outcome: Record the actual outcome.
  • Judgement: Judge whether the prediction matched the outcome.

Testing Experiment 3: How Speed Affects Wavelength

• Use equipment to test the relationship between speed and wavelength.
  • Hypothesis: State the hypothesis.
  • Experiment: Describe the experiment.
  • Prediction: Predict the outcome
  • Outcome: Record the actual outcome.
  • Judgement: Judge whether the prediction matched the outcome.

Relationships of Wave Properties

1. As tension increases, speed increases.
2. As speed increases, wavelength increases.
3. As frequency increases, wavelength decreases.
4. As Amplitude increases, Wavelength does not change.

WAVE EQUATION

• Combine the relationships into an equation:
  • Wavelength = speed / frequency
  • $\lambda = \frac{v}{f}$
  • Units for wavelength are meters.
  • Units for speed are meters/second.
  • Units for frequency are Hertz or 1/seconds.

Testing Experiment 4: Testing the Wave Equation

• Use the simulation to test the wave equation.
  • Hypothesis: State the hypothesis.
  • Experiment: Describe the experiment.
  • Prediction: Predict the outcome
  • Outcome: Record the actual outcome.
  • Judgement: Judge whether the prediction matched the outcome.

MATHEMATICAL MODELS WE HAVE FOR WAVES

• Speed = distance traveled / time taken to travel
• Frequency = number of disturbances / time taken for disturbances
• Wavelength = speed / frequency

Multiple Sources!

• When multiple wavefronts are produced by multiple sources, their amplitudes combine if they are in the same place at the same time.
• Wavefronts do not bounce off each other; they pass through each other and continue moving in their original direction.

Superposition Principle

• When multiple waves pass through the same medium at the same time, the net displacement is the sum of the individual displacements.
  • Mathematically:
    • $y<em>{net} = y</em>1 + y<em>2 + y</em>3 + …$

Interference

• When applying the superposition principle, the amplitude of waves can add constructively (larger amplitude) or destructively (smaller amplitude).
• The process of waves overlapping is called interference.
• Constructive Interference: Results in a larger disturbance.
• Destructive Interference: Results in a smaller disturbance (can result in zero amplitude).

Helpful Simulations for Waves

• Wave Properties:
  • https://phet.colorado.edu/sims/html/wave-on-a-string/latest/wave-on-a-string_all.html
• Superposition/Interference:
  • Qualitative Pulses: https://ophysics.com/w2.html
  • Quantitative Pulses: https://ophysics.com/w2a.html
  • Quantitative Waves: https://ophysics.com/w3.html

WAVES LESSON 4: SOUND, INTRODUCTION

Observational Experiment 1: Generating & Hearing a Sound

• Attach a speaker to a Power Amplifier, change settings to affect how the speaker moves.

Conditions for Generating and Hearing Sound

• Speaker (Source) needs to be vibrating:
  • Above minimum frequency: ~20 Hertz
  • Below maximum frequency: ~20,000 Hz
• Air (Medium) for sound to travel from the source to the receiver.
• Ear (Receiver) of sound.

Sound As A Wave

1. Energy is traveling from the speaker
2. The direction of disturbance of air particles is parallel to direction of movement of the wave fronts.
3. Sound waves are longitudinal waves

Sound Wave PROPERTIES

• Compression:
  • Space where the air is most tightly packed at one moment.
• Rarefaction:
  • Space where the air is least tightly packed at one moment.

Testing Experiment 1: Longitudinal Wave Model

• Hypothesis: In a longitudinal wave, the disturbance moves from one end of a medium to the other, but the individual particles only vibrate back and forth around their initial position.
• Experiment:
  • Disturb a Slinky in parallel to the Slinky and record what you see for one coil that has a piece of blue tape on top of it.
  • Prediction: Predict the outcome.
  • Outcome: Record the actual outcome.
  • Judgement: Judge whether the prediction matched the outcome.

TESTING EXPERIMENT 2: Sound Wave Model (SpongeBass Squarepants)

• Hypothesis: Sound is a longitudinal wave, where the disturbance moves from one end of a medium to the other, but the individual particles only vibrate back and forth around their initial position.
• Experiment: A plush doll is placed in front of speaker.
  • Prediction: Predict the outcome.
  • Outcome: Record the actual outcome.
  • Judgement: Judge whether the prediction matched the outcome.

OBSERVATIONAL EXPERIMENT 2: Characteristics of Sound Waves Experiment

• Attach speaker to power amplifier, change settings one at a time.

1. Loudness depends on Amplitude.
2. Pitch depends on Frequency.
3. Timbre depends on Shape of Wave.

Characteristics of Sound Waves

• Amplitude affects Loudness
  • Larger/Smaller vibrations affect volume.
• Frequency affects Pitch
  • More Frequent/Less Frequent Vibrations affect Pitch.
• Shape of Wave affects Timbre (Quality of Sound)
  • Different types of vibrations affect Tone Quality.

Simulation for Sound Waves

• https://onlinetonegenerator.com/

WAVES LESSON 5: SOUND, ADVANCED

Online Sound Wave Generator

• Use the link below for the experiments this lesson.
• https://onlinetonegenerator.com/
• NOTE: DO NOT EXCEED 500 Hz.

Testing Experiment 1: How Amplitude Affects the Produced Sound

• Hypothesis:
• Experiment:
• Prediction:
• Outcome:
• Judgement:

Testing Experiment 2: How Frequency Affects the Produced Sound

• Hypothesis:
• Experiment:
• Prediction:
• Outcome:
• Judgement:

Testing Experiment 3: How the Shape of the Wave Affects the Produced Sound

• Hypothesis:
• Experiment:
• Prediction:
• Outcome:
• Judgement:

APPLICATION EXP. 1 QUESTIONS

1. Which instrument is like producing higher frequency sound waves? Explain reasoning. Flute.
2. Which instrument do you think is producing higher amplitude wave? Explain reasoning.

Application Experiment 1: Tuning Fork

• Apply our sound ideas to fully explain how tuning forks work.

APPLICATION EXP. 2 QUESTIONS

1. Explains everything you see and hear in the video.

How you would calculate distance to lightning.

• $Speed = \frac{distance traveled}{time taken}$
• $distance traveled = time taken * speed$
• We know Time from the video ~ 6 sec.
• $distance traveled = 6 seconds * SPEED OF SOUND$

Effect of Moving Sources and/or Receivers

Doppler Effect