Vernier Software & Technology

# Stay Tuned: Sound Waveform Models

## Introduction

If you throw a rock into a calm pond, the water around the point of entry begins to move up and down, causing ripples to travel outward. If these ripples come across a small floating object such as a leaf, they will cause the leaf to move up and down on the water. Much like waves in water, sound in air is produced by the vibration of an object. These vibrations produce pressure oscillations in the surrounding air which travel outward like the ripples on the pond. When the pressure waves reach the eardrum, they cause it to vibrate. These vibrations are then translated into nerve impulses and interpreted by your brain as sounds.

These pressure waves are what we usually call sound waves. Most waves are very complex, but the sound from a tuning fork is a single tone that can be described mathematically using a cosine function:

$y = A\cos \left( {B\left( {x - C} \right)} \right)$

In this activity you will analyze the tone from a tuning fork by collecting data with a microphone.

## Objectives

• Record the sound waveform of a tuning fork.
• Analyze the waveform to determine frequency, period and amplitude information.
• Model the waveform using trigonometric functions.

## Sensors and Equipment

This activity features the following Vernier sensors and equipment.

You may also need an interface and software for data collection. What do I need for data collection?

## Real-World Math with Vernier

See other experiments from the lab book.

 1 Walk the Line - Straight Line Distance Graphs 2 Making Cents of Math: Linear Relationship between Weight and Quantity 3 Pool Plunge - Linear Relationship between Water Depth and Pressure 4 Funnel Volumes - Volume and Weight 5 Keep It Bottled Up - Rates of Pressure Increase 6 Mix It Up - Mixing Liquids of Different Temperatures 7 Spring Thing - Newton's Second Law 8 Stretch It to the Limit - The Linear Force Relation for a Rubber Band 9 What Goes Up - Position and Time for a Cart on a Ramp 10 That's the Way the Ball Bounces - Height and Time for a Bouncing Ball 11 Walk This Way - Definition of Rate 12 Velocity Test - Interpreting Graphs 13 From Here to There - Applications of the Distance Formula 14 Under Pressure - The Inverse Relationship between Pressure and Volume 15 Light at A Distance - Distance and Intensity 16 Chill Out: How Hot Objects Cool 17 Charging Up, Charging Down - Charging a Capacitor 18 Bounce Back - The Pattern of Rebound Heights 19 Sour Chemistry - The Exponential pH Change 20 Swinging Ellipses - Plotting an Ellipse 21 Lights Out! - Periodic Phenomena 22 Tic, Toc: Pendulum Motion 23 Stay Tuned: Sound Waveform Models 24 Up And Down: Damped Harmonic Motion 25 How Tall? Describing Data with Statistical Plots 26 And Now, the Weather - Describing Data with Statistics 27 Meet You at the Intersection: Solving a System of Linear Equations 28 Titration Curves: An Application of the Logistic Function 29 Clock Design: Period and Length of a Simple Pendulum 30 Graph It in Pieces: Piecewise Defined Functions 31 Stepping to the Greatest Integer: The Greatest Integer Function 32 Crawling Around: Parametric Plots

### Activity 23 from Real-World Math with Vernier Lab Book

#### Included in the Lab Book

Vernier lab books include word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.