PASCO WA-9611_13 SONOMETER - Manual (Page 16)

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Sonometer 012-03489E
Vibrating
Waveform
Driving
Waveform
Oscilliscope Screen
Figure 1.2 String Vibrations at a
Multiple of the Driving Frequency
Resonant Amplitude Maxima Amplitude Minima
Mode Frequencies (Antinodes) (Nodes)
String length:________________ String tension:_______________ Wire diameter:_______________
Table 1.1
➤ NOTE: The driving frequency of the signal generator may not be
the frequency at which the wire is vibrating. By using a dual trace
oscilloscope, you can determine if the two frequencies are the same,
or if the vibrating frequency is a multiple of the driving frequency,
as shown in Figure 1.2.
➅ From your results, determine and record the wavelength of each
resonance pattern you discovered. (➤ Note that adjacent nodes are
one half wavelength apart.)
➆ Change the string length by moving one or both of the bridges.
Construct a new data table and repeat your measurements for at least
three different string lengths.
Analysis
Using your data, determine the shape of the successive resonance waveforms as the frequency is
increased. How do the wave shapes depend on the length of the string? Sketch the resonance
waveforms for an arbitrary string length. What relationship holds between the wavelength of the
wave and the string length when resonance occurs? Can you state this relationship mathemati-
cally?
For each string length, inspect the frequencies at which resonance occurred. Determine a math-
ematical relationship between the lowest resonant frequency (the fundamental frequency) and the
higher frequencies (overtones) at which resonance occurred.
Optional
➀ Change the string tension by hanging the weight from a different notch. Experiment as needed to
answer the following questions. Do the frequencies at which resonance occurs depend on the
tension of the wire? Do the shapes of the resonance patterns (locations of nodes and antinodes)
depend on the tension of the wire?
➁ Change the linear density of the string by changing strings. Do the frequencies at which resonance
occurs depend on the linear density of the wire? Do the shapes of the resonance patterns (loca-
tions of nodes and antinodes) depend on the linear density of the wire?