(The Speed of Sound, Musical Scales, Short-lasting Sounds)
In this lab, we will dispense with seeing the actual wave on the oscilloscope and, instead, use a program that actually measures the period of the wave and then immediately converts that measurement to a frequency. Access the program Frequency Meter from the
1) hard drive if you are using a stand-alone 386 or 486; select the Physics menu on the
Main menu
2) NCSSM network by selecting Science/Physics/Hardware Interfacing
3) diskette if neither of the above apply
Select M for (Monitor frequency).
Use the microphone attached to the Game Port in the back of the computer (NOT the MPLI blue box).
Part 5: MEASURING THE SPEED OF SOUND
A) Standing waves in open and closed air columns
In the two columns below draw the standing wave pattern of the fundamental (or first harmonic):
OPEN CLOSED
In each case, write down the expression, based on your diagram above, for the length of the air column L in terms of the wavelength of the standing wave.
In each case, determine the frequency of the standing wave in terms of the velocity of the sound wave (v) and the length of the column L.
examples of OPEN tubes are organ examples of CLOSED tubes are
pipes or plastic recorders/flutes organ pipes and 10-cc graduated cylinders
Produce a standing wave by blowing air over the opening of the tube. Measure the frequency of the sound wave, and thereby determine the speed of sound in air in neatly ordered calculations.
Do one example of each tube (open and closed). How can you be sure that the tone that you produce is the fundamental (as assumed in your pictures and calculations above)?
Compare (i.e., % difference) your answer to the known value.
B) Standing waves in solid aluminum
For this part of Lab C7 ONLY, use the MPLI program and microphone (which is the one connected to the light blue MPLI box) and the MPLI software used in the previous lab
C6. Also make sure that you use a 486 computer with the time scale set to the smallest time/division possible (but not "as fast as possible").
Produce a longitudinal standing wave in a vibrating aluminum rod:
Hold the rod exactly at its midpoint, and either
1) strike one end with a metal hammer, or
2) ding against the floor
You may have to wait for a second or two to let the high harmonics die away.
Repeat the procedure in part A (beginning with a diagram) to determine the speed of sound in the aluminum rod.
Compare the experimentally-determined speed of sound with the known value.
Part 6: THE EQUAL-TEMPERED SCALE
The purpose of this part is to investigate the mathematical relationship between successive frequencies of the twelve semitones of an octave.
A) Use the flute setting on the keyboard in order to obtain pure tones. Set the sample time to 1 second. Measure the frequencies of the 13 notes from C4 to C5 and record them in a table in your lab book.
Note Frequency (Hz) Note Frequency (Hz)
C4 G
C# Ab
D A
Eb Bb
E B
F C5
F#
B) Do you see a relationship between the frequency and the number of the semitone? (Hint: consider C4 as 0 and C5 as 12, with the other semitones numbered consecutively; you'll need your calculator.)
Once you come up with a relationship, describe it as specifically as possible. Check this with an instructor or lab assistant.
C) Use your relationship to predict the frequency of a note not measured in your table. Then check your prediction.
D) Using your measurements, calculate the ratios of the frequencies of the following notes. Express the ratios as reduced fractions.
E4:C4 __________ F4:C4 __________ G4:C4 __________ C5:C4 __________
What's special about these ratios (mathematically)? What's special about these tones (musically) when played simultaneously?
Part 7: Whistles, Voices, and Finger Snaps
In this section, we again use the computer as oscilloscope; access this via the Multi-Purpose Lab Interface option from the Physics menu on a 386/486 or from a diskette on a 286. You will now be using the microphone that plugs into the blue MPLI box.
A) So far we have experimented only with the Casio flute sound, which is equivalent to a pure tone (a tone of single, well-defined frequency) which appears as a perfect or near-perfect sine wave on the oscilloscope. We now investigate the wave shapes of other simple sounds. Try whistling, singing a note or the whole scale, blowing air over a pop bottle, striking a tuning fork, or snapping your fingers.
You might also try other instrument options on the Casio (trumpet, organ, etc.).
Which of these sounds is close to a pure tone? Which has the most complicated shape?
B) Another useful feature of the Casio SK-1 is the sampling feature, which allows the user to sample or "save" a sound in the Casio's memory.
Sampling with the Casio SK-1's Built-in Microphone
1) Press the "sampling" button, just below the built-in microphone in the upper right corner of the keyboard.
2) Produce a sound to be sampled near the built-in microphone. Sampling lasts for 1.4 seconds; a sharp metallic click will sound when the sampling operation has ended.
3) Press the "reset" button.
4) Press the "sample" button (just below the "jazz organ" button).
5) Press any of the keyboard keys to hear the sampled sound. (The sound produced will last as long as the original sound, even if the keyboard key remains depressed. To have the original sound continue to be played as long as the key is depressed, press the "loop set" button, and then any of the keyboard keys.)
Try playing the sampled sound with various keyboard keys. Does the wave shape remain the same even though the frequency of the sampled sound changes?
C) Some questions which test your knowledge of what you have learned:
1) After producing a sampled sound of the manner described above and re-playing the sound on several keys, figure out a way to decide which of the keyboard keys produces the same tone as the initial sound. Once you've decided, ask the instructor if you are correct. Describe your method.
2) Use the sampling feature to determine the minimum time between two successive snaps of your fingers. (You may need to snap your fingers three times: once to start the sampling, the other two times for the measurement. In replaying the sound for the oscilloscope period measurement, remember to use only the key decided upon in part 1.
3) Use the same sampled sound to determine the time that a single finger snap lasts.
4) In this portion of the lab you learned that an oscilloscope can do things that a stopwatch can't. What are they?