Experiment 11:

Mechanical Waves and Sound

Objective:

1) To visually observe waves behavior, and

2) examine waves in open and closed pipes

Equipment:

A computer with the Internet connection, a calculator (The built-in calculator of the computer may be used), a few sheets of paper, and a pencil

Theory:

Mechanical waves are two types: longitudinal and transverse.    Longitudinal waves oscillate parallel to their propagation direction.  Transverse waves oscillate perpendicular to their propagation direction.  In this experiment, the fundamental behavior of waves will be studied.

Sound is a longitudinal wave that travels at a speed of v = 331m/s at STP conditions.  A longitudinal wave is one that oscillates parallel to its propagation direction.  The way an induced disturbance travels in a slinky is a longitudinal wave motion.  At a frequency ( f ) that we speak or sing (Audio range: 200Hz – 2000 Hz), the wavelength ( λ ) of a sound wave is in the range of (150cm – 15cm ).  This may be verified by using the wave speed formula:

v = f λ

Resonance of Sound Waves in Open and Closed Pipes

In music, a pipe open at both ends is called an open pipe, and a pipe open at one end only forms a closed pipe as shown below:

Figure 1

Maximum deviation from equilibrium called amplitude for a sound wave can only occur at the open ends of a pipe (if the pipe length is suitable).  This is because of the fact that at an open end of a pipe, air molecules are free to oscillate back and forth.  At a closed end air molecules are not free to perform oscillations.  In other words, closed ends form nodes.   Open ends can form antinodes if pipes have the right lengths for antinodes to occur.

The following figures show how maximum and minimum oscillations occur at open and closed ends for a certain wavelength at different tube lengths:

Figure 2

  Note that, for simplicity, representation of transverse waves are used to show states of maximum and minimum oscillation at open and closed ends.  Sound waves, however, are longitudinal and oscillate back and forth parallel to the tube length and not up and down as shown.  These figures only indicate where maxima and minima occur.

 As can be seen from the figures, the length of a pipe must be multiples of  ( ¼ λ ) for maxima at the open ends to occur.  In an open end pipe, if the length of the pipe is an even multiple of ( ¼ λ ), then the open ends are at maximum states of oscillation, and a load sound is heard.  The pipe is said to be in resonance.   In a closed end tube, the length of the pipe must be an odd multiple of ( ¼ λ  ) for resonance to occur (See the above figures.)

 Wavelength: Wavelength ( λ ) is defined as the distance from one peak to the next peak on a wave.  Of course, in general, wavelength is the distance between two successive points on a wave that are in the same state of oscillation.

 Frequency:  Frequency ( f ) is the number of waves (full λs) generated per second.

Figure 3

Procedure:

Click on the following link:  http://surendranath.tripod.com/Applets.html   On the Applet Menu, hold the mouse on "Waves" and click on "Transverse Waves."

Fill out Tables 1 and 2 below by answering the questions as you progress through different parts of this applet. 

Part 1:

With the wave in "Progressive" mode,

1) Move the "Amplitude" bar on the applet once to minimum and once to maximum (Q₁).  Give an estimate in (cm) of the minimum and maximum amplitude (Q₂).  1 in. = 2.54cm.

2) Set the frequency ( f ) to minimum.  If the whole span of the applet is 24cm, what wavelength do you measure (Q₃)?

3) Set the frequency ( f ) to maximum.  If the whole span of the applet is 24cm, what wavelength do you measure (Q₄)?

With the wave in "Pulsed Crest", observe the wave motion.    Next, with the wave in "Pulsed Trough", observe the wave motion.  The assumption is that you are observing a 24-cm segment of a string infinitely long through which a wave is passing.   Why doesn't the wave return (Q5)?  By return, it is meant "going leftward."

4) Change the mode to "String fixed at both ends."  With the "Amplitude" at any position you want, set the frequency to minimum.  Now, to your opinion, is there a wave moving to the right(Q₆)?  Is there a wave moving to the left (Q₇)?  Do waves get reflected when they hit a harder medium (a fixed point) (Q₈)?  If the answer to Q₈ is "Yes," is a wave that is reflected at a fixed point 180 degrees out of phase with the arriving wave (Q₉)?  Does the reflected wave at the right side fixed point travel to the left (Q₁₀)?  Does the reflected wave at the left side point travel to the right (Q₁₁)?   Is the cause of the wave appearing as a "standing wave" the repeated reflections at both of the fixed ends (Q₁₂)?  With the frequency at minimum, what are the number of antinodes and nodes (Q₁₃)?  With the frequency at the middle, what are the number of antinodes and nodes (Q₁₄)?   With the frequency at the maximum, what are the number of antinodes and nodes (Q₁₅)?

5) Change the mode to "String fixed at one end."  With the "Amplitude" at any position you want, set the frequency to minimum. Now, to your opinion, is there a wave moving to the right(Q₁₆)?  Is there a wave moving to the left (Q₁₇)?  Do waves get reflected when they hit a softer  medium (a free end) (Q₁₈)?  If the answer to Q₁₈ is "Yes," is the reflected wave at a free end in phase with the arriving wave (Q₁₉)?  Does the reflected wave at the right side free end travel to the left (Q₂₀)?  Does the reflected wave at the left side point travel to the right (Q₂₁)?  Is the cause of the wave appearing as a "standing wave" the repeated reflections at both ends (Q₂₂)?  With the frequency at minimum, what are the number of antinodes and nodes (Q₂₃)?  With the frequency at the middle, what are the number of antinodes and nodes (Q₂₄)?   With the frequency at the maximum, what are the number of antinodes and nodes (Q₂₅)?

Table 1:

Part 2:

1. Place the mouse on the "Applet Menu."  Then place it on " Waves."  Click on "Longitudinal waves."

2. In the "Progressive Mode" try the applet on all possible cases of low and high amplitudes along with low and high frequencies.   You will get a good feel and understanding for the motion of longitudinal waves like that of a slinky.

3. With the applet in "Pipe open at both ends" mode, set it on high amplitude and high frequency.  Observe the oscillations for a while.  How many fixed vertical lines do you count?  How many regions of "highest state of oscillations" do you count in between the fixed lines?  In other words, how many nodes and antinodes do you count (Q₁)?  How many (1/4)λ do you count along the pipe length (Q₂)?  How many full λs do you count along the pipe length (Q₃)?  If  the pipe length is 24.0cm, and you counted 2λ along its length, what would each λ or wavelength be (Q₄)? 

4. Now, count the number of oscillations per second, or simply find the frequency, f.   To do this, double-click on the clock of your computer.  You can use your computer's clock to count the number of oscillations per second.  It is better to count the number of oscillations in one full minute, and then divide the result by 60.  AT high frequency, how many oscillations do you count in one minute (Q₅)?  What is the frequency or the number of oscillations per second (Q₆)?

5. Now, knowing λ and f, you can find the wave speed, V, in the pipe on the applet.  Using V = fλ , what is the speed at which the waves travel in the pipe on the applet (Q₇)?

6. Keep the applet in the same mode of "Pipe open at both ends."   Set the frequency at "Low."  How many fixed vertical positions (lines), and how many regions at the highest state of oscillation do you count (Q₈) ?

7. Which one of the 3 cases on the left of Figure 2 above does much with the current state of oscillation of the applet (Q₉)?

8. Set the applet in the "Pipe closed at one end" mode.  Choose "High" amplitude, but "Low" frequency.  How many nodes and antinodes do you count, respectively (Q₁₀)?   Which one of the 3 cases on the right of Figure 2 above does much with the current state of oscillation of the applet (Q₁₁)?

9. How many λ/4 do fit in the pipes length now (Q₁₂)?

10. Is the pipe in resonance (Q₁₃)?  If the pipe is 24.0cm long, and (3/4)λ is filling its length ay any state of oscillation, what is the wavelength of this wave (Q₁₄)?

11. If the pipe is 32.0cm long, with the same wave, what would occur at its open end, a node or an anti-node (Q₁₅)?  Would the pipe then be in resonance (Q₁₆)?

12. If the pipe is 40.0cm long, with the same wave, what would occur at its open end, a node or an anti-node (Q₁₇)?  Would the pipe then be in resonance (Q₁₈)?

Table 2:

Part 3:    (Music)

Harmonics:

Understanding harmonics helps you understand the sound quality better.  The harmonics of a note (a frequency) are integer multiples of that frequency.  For example if a guitar string is oscillating at a fundamental frequency of f = 100Hz, the string is also oscillating at frequencies of 200Hz, 300Hz, and .... as well.  The intensities of the harmonics of a fundamental note are generally weaker than the intensity of the fundamental note itself.  The harmonics of a note give delicacy and quality to the sound of that note.  The quality and beauty of  sound depends on the relative intensity of the participating  harmonics.  We can examine the harmonics of a note as follows:

On the "Applet Menu" scroll down to "Waves" and click on "Harmonics." 

On the applet, set the fundamental frequency at 100% and all Overtones (harmonics) at 0%.  What you see is just the fundamental note.   Let the applet be in the "Fixed at both ends" Mode.  You may observe the applet with or without the "Particle" option as provided at the top of the applet.

Now, set the fundamental frequency at 0% and the first harmonic at 100% with other harmonics at 0%.   You will see that the wavelength halves but the frequency doubles.  Reduce this first harmonic to 50% and you will see that its amplitude that is a measure of the sound strength and intensity reduces to half.

Now, set the second harmonic at 100% with other harmonics and the fundamental at 0%.  You will see that the wavelength becomes 1/3 of the fundamental one, but its frequency triples.   Again reduce the amplitude to say 50% and observe the effect.

Now, set the third harmonic at 100% with other harmonics and the fundamental at 0%.  You will see that the wavelength becomes 1/4 of the fundamental one, but its frequency quadruples.   Again reduce the amplitude to say 50% and observe the effect.

At this point set the fundamental and first harmonic both at 100% with others at 0%, and observe the combination.  After a while reduce the first harmonic to say 60% and observe the effect.

Now set the fundamental, 1st harmonic, and the 2nd harmonic at 100% with the 3rd harmonic at 0% and observe the oscillations.

Next, set all at 100% and observe the waves.  Stop the wave at different instances and observe the shape of its curve.  At any instant, the curve is the sum of 4 curves, the fundamental curve and its 3 harmonics..

Now click on the following applet:   http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=33  

The applet is set at a fundamental frequency of  f =220 Hz.  Turn the speaker on and adjust to a comfortable volume.  Click the "Play" key on the applet.  You will hear the fundamental note.  Add 2f to it by moving the blue circle up with the mouse to about 80% of the way.  See the change in the graph.  Lower the fundamental frequency, f to about 50% and observe the change in the shape of the graph.  Add 3f to it and observe the change.  Add 4f to it and observe the change in the graph.  Keep changing the amplitudes of different harmonics f, 2f, 3f, and 4f and listen to the change in the quality of the sound.  You may go to higher harmonics and even skip one or two or a few and listen to the change in the quality.  At this point you are through with this experiment.  Turn in Tables 1 and 2 as your report with the questions answered.

Data:

N/A                    

           Calculations:

            N/A

Comparison of the Results:

            N/A

Conclusion:  To be explained by students

Discussion:    To be explained by students