Physics 1051 Laboratory #2 Sound and Resonance

Sound Waves and Resonance

Physics 1051 Laboratory #2 Sound and Resonance

Contents

Part I: Objective Part II: Introduction The Nature of Sound Fast Fourier Transform Resonance in Open Tubes End Correction for Real Tubes Speed of Sound in Air Part III: Apparatus and Setup Apparatus Microphone Tuning Fork LoggerPro

Part IV: The Experiment Using the Equipment Predictions Determining the Speed of Sound Part V: Summary

Physics 1051 Laboratory #2 Sound and Resonance

Part I: Objective

In this experiment, you will determine the speed of sound in air by analyzing pressure vs time data collected with a microphone and LoggerPro.

You will also use the relationship and learn about harmonics.

In the above equation, v = speed of sound in air, f = frequency, and

λ = wavelength.

€

v = fλ

Physics 1051 Laboratory #2 Sound and Resonance

Part II: Introduction The Nature of Sound

Sound waves are longitudinal waves. They can propagate in gases, liquids and solids. Sound waves in air travel by the motions of the air molecules as periodic variations in the air pressure with respect to time. A sound wave in air creates regions of high pressure and regions low pressure, as shown below. These regions correspond to the wave crests and troughs, respectively. A sound wave of a single frequency is depicted here. Notice that the pressure varies sinusoidally with respect to time.

Physics 1051 Laboratory #2 Sound and Resonance

Part II: Introduction Fast Fourier Transform

The FFT (Fast Fourier Transform) procedure decomposes a sound wave (pressure versus time data) into its constituent frequencies.

Some sounds consist of only one note, such as the sound produced by a tuning fork. In this case, the FFT of that sound wave would register a single frequency, f, which corresponds to the frequency of that note as shown below.

Physics 1051 Laboratory #2 Sound and Resonance

Part II: Introduction Fast Fourier Transform

Some sounds consist of multiple frequencies some of which may be more intense than others. In this case, the FFT procedure tells you which frequencies the sound contains and the relative amplitudes of each.

Depicted below (left) is a seemingly complex sound wave, consisting of two frequencies of different amplitudes, as well as some low intensity noise.

The plot below (right) is the FFT of the above sound wave showing the two

constituent frequencies.

Physics 1051 Laboratory #2 Sound and Resonance

Part II: Introduction Resonance in Open Tubes

Standing waves may be excited in tubes open at both ends. The waves may be excited by producing a sound at one end of the tube, by blowing across the open end, for example.

The wave patterns are drawn here and the equations for the frequencies are given.

n = 1

n = 2

n = 3 €

f1

=1v

2L

€

f2

= 2v

2L

€

f3

= 3v

2L

The general relationships are: and .

€

λn

=2L

n

€

fn =nv

2L

Physics 1051 Laboratory #2 Sound and Resonance

Part II Resonance in Open Tubes

Normally, there are many standing waves excited at one time and multiple waves will coexist in the tube.

A FFT of the standing wave pattern would show all frequencies present in the tube.

Physics 1051 Laboratory #2 Sound and Resonance

A primary difference between real tubes and ideal tubes is that when standing waves exist in real tubes, a portion of the wavelength actually protrudes a small distance outside the tube.

This is an end correction and makes the tube appear longer than its actual length La. The end correction for a tube of radius r, is given by Lec = 0.61r.

A tube of length La open at both ends will have an end correction for both of the open ends so that the corrected length of the tube is L = La + 2Lec.

This (L= La + 2Lec) is the length you will use in all calculations.

Part II: Introduction End Correction for Real Tubes

La

Physics 1051 Laboratory #2 Sound and Resonance

Part II: Introduction Speed of Sound in Air

The speed of sound in air depends on the ambient air temperature according to

v = 331 m/s + (0.6 m/sºC)TC

where TC is the air temperature in degrees Celsius.

Physics 1051 Laboratory #2 Sound and Resonance

Part III: Apparatus and Setup Apparatus

Microphone Tube Tuning Fork Mallet Metre stick

Physics 1051 Laboratory #2 Sound and Resonance

Part III: Apparatus and Setup Microphone

The ULI microphone is shown in the photograph.

The active element (transducer) is the 9 mm diameter disk located on one end of the plastic case.

The cord should be plugged into the CH1 socket on the LabPro.

Physics 1051 Laboratory #2 Sound and Resonance

Part III: Apparatus and Setup Tuning Fork

Tuning forks emit a pure tone when rung.

The frequency of the tone is stamped on the tuning fork.

Be gentle with the tuning forks and only strike them with the mallet provided!

Physics 1051 Laboratory #2 Sound and Resonance

Launch the LoggerPro program by clicking on the icon below.

It should open with two graphs: !  pressure versus time (spectrum) !  amplitude versus frequency (FFT).

Data will be collected once you click Collect. To end the collection, click Stop.

To erase existing data and begin a new collection, click Collect again.

Part III: Apparatus and Setup LoggerPro

Physics 1051 Laboratory #2 Sound and Resonance

Lab Report

Lab Report 1: Write the objective of your experiment. Lab Report 2: Write the relevant theory of this experiment. Lab Report 3: List your apparatus and sketch your setup.

✏

✏

✏

Physics 1051 Laboratory #2 Sound and Resonance

Part IV:The Experiment Using the Equipment

Goal: In this part of the experiment, you will investigate the sound made by a tuning fork and the sound made by singing.

Use the tuning forks (only hit with the mallet!) to produce sound.

Record the sound using the microphone and LoggerPro.

Physics 1051 Laboratory #2 Sound and Resonance

Part IV:The Experiment Using the Equipment

To accurately read values from the graph, click on your graph to activate it, then click Analyze then Examine.

The values corresponding to the position of the cursor will be displayed. Lab Report 4: Record the frequency (or frequencies) from your FFT

graph. Is this the expected result? Explain.

Trying singing or humming or whistling into the microphone. Lab Report 5: How are the results different from using the tuning

fork? You may wish to include sketches of your graphs.

✏

✏

Physics 1051 Laboratory #2 Sound and Resonance

Part IV: The Experiment Predictions

It will be useful to make some predictions for your data of sound in an open tube.

Assume that the speed of sound in air is 343 m/s.

Record your measurements for tube length and tube diameter. Calculate and record the values of end correction and corrected length (see slide 9) .

Use the corrected length for all calculations.

Lab Report 6: For your pipe, predict the frequencies for the first 5 harmonics. Show your workings and record your results in a table.

Lab Report 7: Sketch the predicted form for the FFT.

✏

✏

Physics 1051 Laboratory #2 Sound and Resonance

Part IV: The Experiment Determining the speed of sound

Goal: In this part of the experiment, you will investigate the resonances within a tube open at both ends.

Lab Report 8: Describe your method of collecting data for determining

the frequencies of the harmonics in the tube. Record your results in a table. Lab Report 9: How do the results from your graph compare to your

predicted results? Explain any differences.

✏

✏

Using the tube and the other apparatus, collect a set of data of sound in the tube.

You may produce sound by blowing gently across the top of the tube.

✏

Physics 1051 Laboratory #2 Sound and Resonance

Part IV Determining the speed of sound

Open Graphical Analysis and plot the appropriate data.

You may display the regression line for this data set: Click Analyze then Linear Fit. Double click on the box that appears and check Show Uncertainty. Format: Include a title and axes labels. Turn off connecting lines.

Print your graph. Lab Report 10: Use your data to determine the speed of sound in air and

its uncertainty. Lab Report 11: Compare your value of the speed of sound to the

theoretically predicted value calculated using the temperature dependence.

✏

✏

Physics 1051 Laboratory #2 Sound and Resonance

Part V: Summary

Lab Report 12: Outline briefly the steps of your experiment. Lab Report 13: List your experimental results and comment on

how they agreed with the expected results. Lab Report 14: List at least three sources of experimental

uncertainty and classify them as random or systematic.

✏

✏

✏

Physics 1051 Laboratory #2 Sound and Resonance

Wrap it Up!

Make sure that you have answered all the Questions completely.

Be sure to include your printed graph.

✏