Vernier Software & Technology

# Sound Waves and Beats

## Introduction

Sound waves consist of a series of air pressure variations. A Microphone diaphragm records these variations by moving in response to the pressure changes. The diaphragm motion is then converted to an electrical signal. Using a Microphone and an interface, you can explore the properties of common sounds.

The first property you will measure is the period, or the time for one complete cycle of repetition. Since period is a time measurement, it is usually written as T. The reciprocal of the period (1/T) is called the frequency, f, the number of complete cycles per second. Frequency is measured in hertz (Hz). 1 Hz = 1 s–1.

A second property of sound is the amplitude. As the pressure varies, it goes above and below the average pressure in the room. The maximum variation above or below the pressure mid-point is called the amplitude. The amplitude of a sound is closely related to its loudness.

In analyzing your data, you will see how well a sine function model fits the data. The displacement of the particles in the medium carrying a periodic wave can be modeled with a sinusoidal function. Your textbook may have an expression resembling this one:

$y = A sin (2 \pi f \text{ }t)$

In the case of sound, a longitudinal wave, y refers to the change in air pressure that makes up the wave, A is the amplitude of the wave, and f is the frequency. Time is represented by t, and the sine function requires a factor of 2π when evaluated in radians.

When two sound waves overlap, air pressure variations will combine. For sound waves, this combination is additive. We say that sound follows the principle of linear superposition. Beats are an example of superposition. Two sounds of nearly the same frequency will create a distinctive variation of sound amplitude, which we call beats.

## Objectives

• Measure the frequency and period of sound waves from a keyboard.
• Measure the amplitude of sound waves from a keyboard.
• Observe beats between the sounds of two notes from a keyboard.

## Sensors and Equipment

This experiment 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?

## Physics with Vernier

See other experiments from the lab book.

 1 Graph Matching 2A Back and Forth Motion 2B Back and Forth Motion 3A Cart on a Ramp 3B Cart on a Ramp 4A Determining g on an Incline 4B Determining g on an Incline 5 Picket Fence Free Fall 6 Ball Toss 7 Bungee Jump Accelerations 8A Projectile Motion (Photogates) 8B Projectile Motion (Projectile Launcher) 9 Newton's Second Law 10 Atwood's Machine 11 Newton's Third Law 12 Static and Kinetic Friction 13 Air Resistance 14 Pendulum Periods 15 Simple Harmonic Motion 16 Energy of a Tossed Ball 17 Energy in Simple Harmonic Motion 18A Momentum, Energy and Collisions 18B Momentum, Energy and Collisions 19A Impulse and Momentum 19B Impulse and Momentum 20 Centripetal Accelerations on a Turntable 21 Accelerations in the Real World 22 Ohm's Law 23 Series and Parallel Circuits 24 Capacitors 25 The Magnetic Field in a Coil 26 The Magnetic Field in a Slinky 27 Electrical Energy 28A Polarization of Light 28B Polarization of Light (Rotary Motion Sensor) 29 Light, Brightness and Distance 30 Newton's Law of Cooling 31 The Magnetic Field of a Permanent Magnet 32 Sound Waves and Beats 33 Speed of Sound 34 Tones, Vowels and Telephones 35 Mathematics of Music

### Experiment 32 from Physics 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.