1
Physics 1021
Experiment 3
Sound and Resonance
2
Physics 1021
Experiment 3
Sound and Resonance
Introduction
◉
In today's experiment, you will examine beat frequency using tuning
forks, a microphone and LoggerPro.
◉
You will also produce resonance in a tube open at both ends and use
your results to determine the speed of sound in air.
◉
Finally, you will compare the resonances in a tube open at both ends to
the resonances in a tube open at one end.
Sound and Resonance
Fast Fourier Transform (FFT)
Sound waves in air travel as pressure variations caused by motion of the air
molecules. The pressure variations are sinusoidal with time.
Taking the Fast Fourier Transform of a sinusoidal wave shows the
frequency of that wave.
EXAMPLE: A tuning fork produces a sinusoidal pressure wave as is shown
below. Taking the FFT indicates the frequency of the wave which is the
same as the frequency of the tuning fork.
Amplitude
3
Physics 1021
Experiment 3
If a sound wave is composed of many frequencies, the FFT will show all
frequencies present in that sound.
4
Physics 1021
Experiment 3
Sound and Resonance
Beats - Apparatus
Microphone
Mallet
2 tuning forks
- 512 Hz
- 480 Hz
The active element (transducer)
is the 9 mm diameter disk located
on one end of the plastic case.
To detect sound, point the end of
the microphone directly at the
sound source.
!
The cord should be plugged into
the CH1 socket on the LabPro.
UPDATE THIS PIC
5
Physics 1021
Experiment 3
Sound and Resonance
Beats - Experimental Method
Launch the LoggerPro program by clicking on the icon below.
CLICK HERE
CLICK HERE
It should open with two graphs: pressure versus time and amplitude versus
frequency (FFT).
Ring one tuning fork near the microphone and click Collect.
!
Only strike the tuning fork with the mallet!
The top graph is called the waveform. It is a sinusoidal graph. It has a
distinct period and therefore a distinct frequency.
6
Physics 1021
Experiment 3
Sound and Resonance
Beats - Understanding the FFT
!
Highlight the peak to peak distance of five oscillations of your waveform as
shown.
NOTE: You can Autoscale your graph by clicking on the blue “A” in the bar
above the FFT.
7
Physics 1021
Experiment 3
Sound and Resonance
Beats - Understanding the FFT
LW
LW
LW
◉
Record the total time in Table 1.
◉
Using the total time, determine the period of the oscillation and record
this in Table 1.
◉
Using the period, determine the frequency of the oscillation and record
this in Table 1.
The total time for the five oscillations
is given as Δ𝑡 in the lower left
hand corner of graph.
8
Physics 1021
Experiment 3
Sound and Resonance
Beats - Understanding the FFT
The lower graph is the FFT or spectrum. It shows the frequency present in
the waveform.
Activate the FFT graph by clicking on it.
!
Click Analyze then Examine. Move the mouse over the peak on the
spectrum. The value of the frequency is displayed in the pop-up box.
Q
QUESTION 1: According to the spectrum:
a) What is frequency present in the waveform?
b)
Does this value agree with your frequency calculated in Table 1?
c)
Do they both agree, within a few hertz, with the value stamped on
the tuning fork?
9
Physics 1021
Experiment 3
Sound and Resonance
Measuring the beat frequency
◉
◉
◉
◉
Click Collect in LoggerPro.
Ring two tuning forks at the same time using the mallet. Keep the forks
as close to each other as possible without touching. You may need a few
tries to get this to work.
Hold them both near the microphone.
The FFT graph should show the two frequencies of your tuning forks with
about the same amplitudes. If they do not, repeat the data collection until
they do.
10
Physics 1021
Experiment 3
Sound and Resonance
Measuring the beat frequency
Q
QUESTION 2: Sketch the waveform. Indicate the period of the beats on the
sketch.
!
Highlight one cycle of the oscillation and find the beat period.
Q
QUESTION 3: Using the beat period, determine the beat frequency and its
uncertainty.
Q
QUESTION 4: Find the predicted beat frequency using the frequencies
stamped on the tuning forks. Do the values agree?
Comment.
11
Physics 1021
Experiment 3
Sound and Resonance
Resonance in a tube - Apparatus
!
The procedure for this part is shown in the photographs. Hold the microphone
at one end of the tube and blow across the other end.
12
Physics 1021
Experiment 3
Sound and Resonance
Resonance in a tube - Predictions
Q
QUESTION 5: Why there are multiple peaks in the FFT graph?
Q
QUESTION 6: What do you expect for the shape of a f vs n graph? Explain.
Q
QUESTION 7: Write an equation for the slope of a f vs n graph. What do
you expect for the intercept? Explain.
!
Refer to plotting and interpreting graphs section in the introduction. You are
not supposed to use your data to answer this question.
LW
Using the metre stick, measure the length and inner diameter of your tube.
Record your results in Table 2.
13
Physics 1021
Experiment 3
Sound and Resonance
Resonance in a tube - Experiment
Launch the LoggerPro program by clicking on the icon below.
CLICK HERE
!
CLICK HERE
It should open with two graphs: pressure versus time and amplitude versus
frequency (FFT).
◉ Click Collect.
◉ Blow gently across one
end of the tube while
holding the microphone
at the other end.
◉ When you have
recorded satisfactory results, click Stop.
◉ Your FFT graph will look like the one shown above.
◉ From the top menu bar, choose Experiment → Store Latest Run.
14
Physics 1021
Experiment 3
Sound and Resonance
Resonance in a tube - Data
Activate the FFT graph by clicking on it. Click the
button and use the
cursor to determine the frequencies of the observed harmonics.
Note: The first resonance is called the 1st harmonic. If the second
resonance has twice the frequency of the first then it is labeled the 2nd
harmonic (𝒏 = 𝟐). 𝒏 is called the harmonic number.
LW
Record the frequencies and harmonic number of the observed harmonics in
Table 3 of your Laboratory workbook.
15
Physics 1021
Experiment 3
Sound and Resonance
Resonance in a tube - Analysis
◉
Launch Graphical Analysis by clicking on the icon below.
CLICK HERE
CLICK HERE
◉
Plot frequency versus harmonic number for your pipe.
◉
Create a linear fit to your graph by clicking Analyze then Linear Fit.
◉
Find the uncertainty in your slope and intercept by double clicking on the
pop up box and checking the option to “Show uncertainty”.
◉
Record the slope, intercept, and uncertainties in Table 4.
◉
Print your graph by clicking Print then Print Graph.
LW
P
16
Physics 1021
Experiment 3
Sound and Resonance
Resonance in a tube - Analysis
Q
QUESTION 8: Use your slope and your result from Question 6 to determine
the speed of sound in air. Don’t forget units and uncertainty.
Using the equation from the introduction and the room temperature
displayed on the laboratory screens, determine the theoretical value for the
speed of sound in air.
Q
QUESTION 9: Are the two values equal within the uncertainty? Comment.
Q
QUESTION 10: How does your intercept compare to your expected value?
Explain.
Q
QUESTION 11: Sketch the standing wave pattern for the first 4 resonances
for a tube open at both ends. Indicate whether sketches are
of pressure or displacement waves.
17
Physics 1021
Experiment 3
Sound and Resonance
Resonance in a tube open at one end
◉
LW
!
◉
Cap one end of the tube and by gently tapping the endcap, obtain a new
FFT (It will superimpose itself on your first FFT).
Record your frequency results in Table 5.
Carefull! You will need to assign values of 𝒏.
Hint: The 5th harmonic (𝒏 = 𝟓) has a frequency which is 5 times the
frequency of the 1st harmonic.
Q
QUESTION 12: How does the fundamental frequency (1st harmonic) in the
tube open at one end compare to the fundamental
frequency of the tube open at both ends?
Q
QUESTION 13: How does the frequency spectrum in the tube open at one
end compare to the frequency spectrum of the tube open at
both ends, i.e. are all the harmonics present in both cases?
18
Physics 1021
Experiment 3
Sound and Resonance
Summary
Q
QUESTION 14: Summarize the two main differences between a tube open
at both ends and a tube open at one end.
Q
QUESTION 15: List one source of systematic uncertainty in this experiment.
List one source of random uncertainty in this experiment.
19
Physics 1021
Experiment 3
Sound and Resonance
Wrap it up!
✔ Check that you have completed all the Tables of your Laboratory
workbook.
✔ Make sure that you have answered all the Questions completely.
✔ Attached to your Laboratory workbook should be the following
graph:
✔ Frequency vs Harmonic Number (Graphical Analysis)
!
Don’t forget to sign out!