May 13, 1996
In this section you must use a computer with an attached Multi-Purpose Lab Interface (light blue) Box; a microphone should be plugged into the MPLI Box. The entire apparatus will function as an oscilloscope. If you have a 386/486 hard-drive, access the software from the Main Menu by choosing Physics, then Multi Purpose Lab Interface; if you have a 286, access the software from a diskette.
Choose the L option (Oscilloscope). Familiarize yourself with various options by typing ? to access the Help Menu. Several of the important commands include H, <space bar>, Left and Right arrow keys, Up and Down Arrow keys.
We will use the Casio SK-1 keyboard to produce sound. Appendix 1 contains additional information on the Casio keyboard, including the frequencies of various notes that the Casio produces. A microphone will convert the sound to a voltage signal that the computer recognizes. Remember that the oscilloscope produces a voltage-versus-time plot.
For this part we need a pure sine wave, i.e., a wave of a single frequency. Produce this on the Casio by choosing the flute sound and then depressing any white or black key. You may notice that the loudness of the sound oscillates slightly; turn this annoying vibration off by depressing the vibrato button once. The Casio will continue to produce a flute sound until it is turned off or until another "musical instrument" button is depressed.
Depress (and continue hold down) any black or white key. Vary the volume control on the keyboard. What happens to the wave on the oscilloscope screen? Try another key and again vary the volume control. Conclusions? Can you increase the apparent amplitude of the wave on the screen in a way other than changing the volume control? How?
Play a complete octave of notes (an octave consists of eight successive white keys) in sequence. How does the wave pattern change as the scale is played? Does the wave shape change from note to note? Does the amplitude change from note to note? [NOTE: amplitude and frequency are, in general, independent. Unfortunately, the Casio manufacturers have produced a keyboard in which the sound does change in amplitude - and therefore loudness - with a change in frequency.]
In this part, you will measure the frequency of "concert A" note, produced by depressing the key labeled A4. Refer to the labeled keyboard diagram in Appendix 1. We will determine the frequency by measuring the period of the wave. Continue to use the flute sound in this part.
A) In order to obtain the most accurate measure of the period, how many cycles
should be displayed on the oscilloscope screen? Why? Use the arrow keys to so
adjust the display.
note that when making measurements along the time scale, the MPLI software cannot be set to "as fast as possible"; it must be set to one of the scales such as " 5 ms/division "
B) After you use the H command to hold the wave pattern, a cursor will appear. Use the
cursor to determine the time that one period (or one complete wave cycle)
covers. Draw and label a diagram below that shows the full screen and the two
cursor positions you used to measure the period.
C) Determine the frequency from your result in part B.
D) Determine the frequency of the A5 note that it is one octave above A4. Show
measurements and calculations in a neat and organized manner.
E) Determine the frequency of the A3 note that it is one octave below A4. Show
measurements and calculations in a neat and organized manner.
F) What general conclusions can you make about the frequency of notes that are
an octave apart?
A) In class, we showed how to determine the sum of two waves with frequency 17
and 14. Draw the predicted sum of two sine waves of frequency
a) 18 and 14
b) 6 and 7
B) Label the beat period ( = reciprocal of the beat frequency) and the period
associated with the wave average frequency (of the two added waves).
C) Access the program WAVES either on the NCSSM network (under Physics) or on
a 386/486 physics computer (from Main, Physics Tutorial, Network Physics
Programs, Waves)
D) Choose Wave Addition and verify your two predicted graphs below.
A) Depress the F3 and F3-sharp keys simultaneously. The F3# key is the black key
to the right of the F3 key. Adjust the time per division with the arrow keys until
wave pattern on the computer looks similar to the pattern obtained in part 1 with
the Wave addition program.
Your screen should look something like
In Figure 1, the addition of a wave of frequency 11 Hz and of a wave of frequency 9 Hz result in a wave of frequency 10 Hz (the average of the two individual frequencies) that peaks in amplitude (i.e., constructive interference, CI) with a frequency of 2 Hz. Equivalently, the period of these beats is 0.5 second; note the time scale at the bottom of the figure.
B) Measure the beat frequency of the F3/F3# combination using the method
introduced in Part 2. Show measurements and calculations in an orderly
manner.
C) Try to measure the beat frequency aurally using your watch or a clock. What
result do you get and how does it compare with that in part B?
D) Calculate the expected beat frequency, using the known frequencies of F3/F3#
notes; see Appendix 1. % difference?
E) Experimentally determine what happens to the beat frequency if you depress two
keys together that are farther apart in frequency (e.g., F3 and G3 or F3 and G3#).
Sketch your observations and draw appropriate conclusions.
F) Experimentally determine what happens to the beat frequency if you depress two
adjacent keys that are much higher up the scale. Sketch your observations and
draw conclusions.
The numbers refer to the octave in which they belong on a standard 88-key piano. The lowest note on the piano keyboard is called C0 and has a frequency of 16 Hz; it is followed by the notes D0 E0 ... The next C note reached (the eighth white key after the first) begins the next octave and is termed C1; it has a frequency twice that of C0, i.e., 32 Hz. The highest note on an ordinary piano is B8 with a frequency of 7902 Hz. Notice that the Casio keyboard therefore covers the same notes as the middle part of a piano keyboard.]
The black keys are named according to one of the white keys they adjoin. The black key to the immediate right of C4 is called C-sharp (and written C#) and produces a sound of frequency 277.2 Hz; it may also be termed D-flat, since it is to the immediate left of D4. "Sharp" notes are slightly higher than their white key namesakes; a "flat" note is a slightly lower frequency than its namesake.
[SPECIAL NOTE: The Casio keyboard designers have not been entirely consistent in generating frequencies for the different musical instruments provided. For the flute, trumpet, brass, pipe organ, and voice settings, the frequencies of the notes are given by the keyboard diagram above. For the piano setting, the frequencies of the notes are all two times higher (or, equivalently, one octave higher) than those given in the keyboard diagram above. For the jazz organ setting, the frequencies of the note are all one-half (or one octave lower than) those given in the keyboard diagram above.]
power off.....Keyboard power OFF.
play.....For normal keyboard play, One Key play, or Memory play.
3) Power indicator
Lights when unit power is switched ON.
4) Mode selector
normal.... 4-note polyphonic
solo 1 ..... Monophonic (with multi track memory)
solo 2 ..... Monophonic (with multi track memory)
chord ...... Accompaniment (with multi track memory)
5) Volume control
Control volume level.
6) Portamento ON/OFF button
Switches portamento effect ON and OFF.
7) Vibrato ON/OFF button
Switches vibrato effect ON and OFF.
8) Synthesizing button
Used when creating sounds using harmonic synthesis.
9) Envelope select button
Applies one of the 13 available envelopes to each tone.
10) Tone selectors
Used to select the desired tone.
11) Tempo control
Controls rhythm tempo. Each press of button increases tempo, while each press of decreases tempo.
12) Rhythm button
Press to allow selection of one of the 11 auto-rhythms using rhythm selector buttons. The rhythm will start the moment the rhythm selector button is pressed.
13) Fill-in button
Inserts a fill-in (rhythm grace) into the music during play.
14) Demo (demonstration) button
Plays a preset demonstration piece (Toy Symphony).
15) Clear button
Clears the previous memory contents. Set the functions selector to "record" and then press clear to prepare memory for new input.
16) Delete button
Used to clear errors from a melody in memory.
17) Auto play button
Plays back melody stored in memory.
18) Reset button
Press after storing a melody into memory.
19) One Key Play buttons
Play one note of the melody stored in memory with each press.
20) Sampling button
Begins sampling (recording).
21) Built-in microphone
Used to pick up sampled sound.
22) Loop set button
Press to make sampled sound continuous.
23) Chord selector keys
Produce the indicated chord when the mode selector is set to chord.
24) Envelope selector keys
Used to select the desired envelope after the envelope select button is pressed.
25) Rhythm selector keys
Used to select the desired rhythm after the rhythm selector button is pressed.
26) Foot selector keys
Used to select the desired harmonic synthesis after the synthesizing button is pressed.
