Make-up lab

Sound

Vibrating objects can produce sound.  Sound waves are longitudinal waves.  They can travel through solids, liquids and gases.  In this laboratory you will visualize the patterns of pressure variations associated with different sounds traveling through air and you will examine the frequency content of those patterns.  You will also examine standing sound waves in a tube and measure the speed of sound waves in air.

Open a Microsoft Word document to keep a log of your experimental procedures, results and discussions.  Address the points highlighted in blue.  Answer all questions.

Exercise 1

Produce a sound pulse by clapping your hands once.

• What do your hands do to produce this sound?
• How does the sound reach your ears?

Sound is a pressure variation that propagates through a gas or solid. 
Consider a long, gas-filled cylinder with a piston on one end.

• (a)  The pressure is uniform throughout the cylinder.  Denote this pressure by P₀.
• (b)  The plunger is pushed quickly into the cylinder.  This causes a compression of the gas molecules near the plunger.
• (c)  The plunger is quickly pulled back out of the cylinder.  This causes a rarefaction of the gas molecules near the plunger.
• (d)  The compression/rarefaction pattern moves down the cylinder.

Note:  While the pressure variation travels down the cylinder, the gas particles do not.  They move back and forth over a relatively small distance.

Sketch pressure in the cylinder as a function of position along the cylinder axis for the figures (a) and (b) to the right.

This Word document contains the figures.  Choose insert Shapes Lines, Scribble, and then sketch with the mouse.

Experiment 1

Most sounds we hear are not single sound pulses but more complex sound patterns.  We will now explore some of those sound patterns.

(a)  Compare the output of your computer's microphone for a clapping and a humming sound.  The microphone converts pressure variations into voltage variations which can be recorded and displayed by the computer.

• Open the Virtual Oscilloscope web page.  When asked, allow this page to access your microphone.  The oscilloscope's input, by default, is the live voltage output of your microphone.  When the program starts, the output is probably due to background noise.
• Explore the interface.  You can adjust the oscilloscope's vertical scale (Volts/div) and horizontal scale (Seconds/div).  You can also adjust the gain, to amplify the microphone signal.  You can freeze the live input at any time.
• Clap your hands together.  What does the output look like?
• Make a continuous humming sound, for example "ahhhh".  Adjust the scales until you are satisfied with the oscilloscope representation of the sound.  (You can do this before or after you have frozen the live input.  Describe some of the characteristics of the sound pattern.  Does your humming sound wave have a definite frequency?  How do you justify your answer?

(b)   Examine the output of your computer's microphone for the sound produced by a tuning fork.

• You probably do not have a tuning fork, so let us generate the pure tuning-fork sound using this online tone generator.
• Choose a sine wave, pick a frequency, and play the tone.  (You can play it on the same computer, or you can open the tone generator on another device.)
• Freeze the input and adjust the "time and voltage scales until you get a good display of several cycles of the signal on the oscilloscope.
• Screen capture the pattern and paste it into your log.  Describe the pattern.  Does the tone generator producing a pure sine wave?  How does the waveform of the tone-generator sound compare to the waveform of the humming sound?
• Repeat the procedure (without screen capture) for different frequencies and compare the patterns.
• You may also want to listen to and look at the wave patters the tone generator produces if you choose a square, saw-tooth, or triangle wave.

(c)  Any wave pattern can be produced by superimposing the appropriate sinusoidal waves.  Breaking up the original sound wave into its sinusoidal components is called Fourier analysis.  We can find the frequencies and amplitudes of the sine and cosine waves that must be added to produce our sound wave by letting the computer perform a Fourier analysis on the sound.

• Close the oscilloscope and open the microphone sound analyzer program.  Click "Yes" to let compadre.org use your microphone.
• Choose "Show: both at the top.  You can adjust the vertical scale by typing different numbers in the "Amp Scale" text box at the bottom.
  Pressing play records the sound signal, and pressing pause freezes it.  (Do not record for a long time, or the display will slow down.)
• The bottom window displays the live voltage output of your microphone.
• The top window displays a Fast Fourier Transform or FFT of this signal.  It shows the relative amplitudes of the sine waves of different frequencies that are superimposed to make the sound.
  Note: The scale is in dB, so if the audio level at a frequency 1 is twice the audio level at a frequency 2, the sound intensity at frequency 1 is 10 times that at frequency 2.
• Obtain a Fast Fourier Transform of a sine wave signal at 440 and 1000 Hz produced by the tone generator.  Does it look like you would expect it to look?
• What changes if you let the tone generator play a square, a saw-tooth, or a triangle wave.  Describe the FFT patterns.
• Click play and start humming an  "ahhhh" sound.  When you have a stable signal pause.

• Screen capture and paste your graph into your log.  What frequencies are strong in your "ahhh" sound?  Without changing the pitch of your voice, change the sound from "ahhhh" to "eeee".  What happens to the frequencies shown in the FFT display?

Experiment 2

Watch this Tube Resonance video.

Measure the speed of sound

Assume you had followed the procedure outline below to make measurements using a resonance tube and two tuning forks.  With a magnet you can move a piston inside the resonance tube to adjust its length.  The maximum length is 1 m.  The tube has one open and one closed end.  For a fixed frequency you can produce several resonances by varying the length of the tube.  The closed end of a tube is a node in the longitudinal displacement.  The open end of a tube is approximately an antinode in the longitudinal displacement.

Procedure:

This is the procedure that was followed to obtain the data in table 1.

• Pick one of the tuning forks.  The frequency f with which it oscillates is stamped on the fork.  Strike the tuning fork against a rubber block.
• Hold the fork near the open end of the resonance tube.  Start with a zero-length tube and move the piston until you find the 1st harmonic. 
  You will hear the loudest sound and you will also see the maximum peak voltage on the oscilloscope display.
• Record the tube length for the 1st harmonic in table 1.
• Move the piston until you find the 3rd harmonic.  Record the tube length for the 3rd harmonic in table 1.
• Move the piston and look for the the 5th harmonic?  If you find it, record the tube length for the 5th harmonic in table 1.
• Measure the air temperature and record it in table 1.
• Repeat the experiment with the other tuning fork.  Table 1 now contains your data.

Table 1

(tube length (m)))

Analyze the data and complete table 2. 

The displacement nodes of standing waves in a tube are well defined, while the displacement antinodes at the ends can be displaced by a small distance from the actual ends of the tube.  So it is best to use the distance between antinodes to to find the wavelength λ,

Table 2

Compare your experimentally obtained value for the speed of sound with the value obtained from the formula
v = (331.4 + (0.6/^oC)T_C) m/s.