General Physics I Lab
M10 Standing Waves on a Vibrating String
General Physics I Lab
M10 Standing Waves on a Vibrating String
Purpose
In this experiment, you will investigate standing waves created on a vibrating string.
Equipment and components
Sonometer, driver and detector coils, bridge (x2), Science Workshop 750 interface as
function generator, masses and hanger, dual trace oscilloscope, micrometer, set of strings:
String Diameter ∅ ( in/mm )
Linear Density μ ( kg/m )
0.010 /0.2540
0.014 /0.3556
0.017 /0.4318
0.021 /0.5334
0.023 /0.5842
0.39 x 10-3
0.78 x 10-3
1.12 x 10-3
1.50 x 10-3
1.84 x 10-3
Background
Standing waves are created in a vibrating string when a wave is reflected from one end of the
string so that the returning wave interferes with the original wave. The standing wave has
nodes, where the string does not move, and antinodes, where the string vibrates up and down
with maximum amplitude. Actually, the wave will be reflected many times back and forth
between the two ends of the string, and all these multiple reflections will interfere together. In
general, the multiply reflected waves will not all be in phase, and the amplitude of the wave
pattern will be small. However, at certain frequencies of oscillation, all reflected wave are in
phase, resulting in a very high amplitude standing wave. These frequencies are called
resonant frequencies. In this experiment, you will study resonance modes of the standing
wave on a stretched string, determine the shape of the successive resonance waveforms, and
measure the velocity of wave propagation on the string.
Procedure
Experiment setup
1. Set up the sonometer and connect the circuit as shown in Figure 1.
Figure 1 Experimental setup
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General Physics I Lab
M10 Standing Waves on a Vibrating String
2. Start with the bridges 60 cm apart. Use the string with diameter = 0.017 inch.
3. Use the micrometer to measure the diameter of the string (in mm) to ensure the right
string is used and look up the table in “Equipment and components” section.
4. Hang a mass of 0.8 kg to the slot 3 of the tensioning lever. Adjust the string adjustment
knob so that the tensioning level is horizontal.
5. Position the driver coil approximately 5 cm from one of the bridges and position the
detector near the center of the wire.
6. Open the “M10” program in the course folder.
• The program will open with a Signal Generator dialog box and use the 750 interface
as a signal generator. Use the Signal Generator dialog box to choose the type of
wave, and control the amplitude and frequency output.
• Adjust the amplitude and frequency with the plus (+) and minus (-) buttons
(as shown in Figure 2) or type in a numerical value directly. Use the arrows for
stepped progression.
7. Set the signal generator to produce a sine wave with amplitude = 2V and
frequency = 10Hz.
8. Set the gain of the oscilloscope to an appropriate value of Volt/Div and select channel 1
as the triggering source.
Figure 2 Signal Generator dialog box
Part I: Resonance modes
1. Record the string’s length (L), tension (T), and linear density (μ) in Table 1.1 in the lab
report. As shown in Fig. 3, the string tension is determined by multiply the weight (Mg)
of the hanging mass by 1, 2, 3, 4, or 5, depending on which notch of the tensioning lever
the mass is hanging on.
2. Slowly increase the frequency of the driving signal for the driver coil, starting at 30Hz in
step of 1Hz. Listen for an increase in the volume of the sound from the sonometer and/or
observe an increase in the amplitude of the detector signal on the oscilloscope screen.
Frequencies that result in maximum string vibration are resonance frequencies.
3. Find the lowest frequency at which the resonance occurs. This is the resonance in the
first, or fundamental, mode. Record this frequency in Table 1.1.
NOTE: - The driving frequency from the signal generator may not be the same as that 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 (in most of the cases), as shown in Figure 4.
- When near the resonance occurs, change the frequency increment to 0.1Hz to
fine tune the driving frequency (this accuracy is adequate in the experiment).
This is helpful in finding the maximum vibration on the string.
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General Physics I Lab
M10 Standing Waves on a Vibrating String
Figure 3 Setting the tension
Figure 4 String vibration at a multiple
of the driving frequency
4. Observe the standing wave in the string at the same horizontal surface as the string while
the resonance occurs. Locate and record the locations of each node and antinode. Record
your results in Table 1. (Hint: Adjust the amplitude of the driving signal to optimize the
standing wave.)
5. Continue to increase the driving frequency to find successive resonant frequencies (at
least three). Record the resonant frequency of each mode and the locations of nodes and
antinodes in Table 1.
NOTE: - If the detector is placed too closed to the driver, it will pick up some
interference. For best results, keep the detector at least 10cm from the driver.
- Place the detector to an appropriate position for searching higher resonance
modes.
6. From your results, determine and record the wavelength of each resonance pattern you
discovered.
NOTE: Adjacent nodes are one half wavelength apart.
Part II: Velocity of wave propagation
1. Setup the sonometer with the string of diameter = 0.017 inch and hang the mass on slot 1.
Attention: Whenever you change a string, place the used one back in its bag before
taking out another string to avoid mixing up the strings.
2. Slowly increase the driving frequency of the driver coil, starting with a frequency of
10Hz and step of 1Hz. Find the lowest frequency at which the resonance occurs. Record
this value in Table 2.
3. Also record the string’s length (L), tension (T) and linear density (μ) in Table 2.
4. Change the string tension by moving the hanging mass to different notches. Repeat steps
2 and 3 for three different values of the string tension.
NOTE: Adjust the string adjustment knob to ensure the tensioning level is horizontal
5. Set the string tension to an intermediate value (hanging mass at slot 3). Then repeat steps
2 and 3 using two other different strings.
6. Use the measured string length, the fundamental frequency and the equation
(Velocity = Wavelength × Frequency), to determine the velocity of the wave on the
string for each value of tension and linear density that you used. Record your results in
Table 2.
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General Physics I Lab
M10 Standing Waves on a Vibrating String
Name
Date
Lab session
(Day & time)
Lab partner
M10 Standing Waves on a Vibrating String Lab Report
A. Answer the following questions BEFORE the lab session (6 pts each)
1. Sketch three lowest normal modes of a standing wave in a string fixed at both ends.
Indicate the location of the nodes and antinodes.
2. What relationship holds between the wavelength of the standing wave and the string
length when resonance occurs?
3. Determine a mathematical relationship between the lowest resonant frequency (the
fundamental frequency) and the higher frequencies (overtones) at which resonance
occurred.
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General Physics I Lab
M10 Standing Waves on a Vibrating String
B. Results and data analysis
Part I: Resonance modes
Table 1 (25 pts)
String length L: ____________
Linear density μ: __________
Mode
Resonant
frequencies (Hz)
(detector)
String tension T: _____________
Amplitude maxima
position (m)
(Antinodes)
Amplitude minima
position (m)
(Nodes)
Wavelength
(m)
Part II: Velocity of wave propagation
Table 2 (25 pts)
String length L:__________
Tension, T
(
)
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Linear density, μ
(
)
Fundamental
frequency ( )
Wave velocity, V
(
)
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General Physics I Lab
M10 Standing Waves on a Vibrating String
C. Answer the following questions after the experiment
4. Assume that the velocity of wave propagation (V) on a stretched string depends only on
two variables: the linear density of the string μ (mass per unit length) and the tension of
the string (T). Use dimensional analysis to show how V changes with μ and T. (6 pts)
5. Verify the relationship you derived in (4) using the data shown in Table 2. (Hint: plot V
as a function of a combination of μ and T, so that the final curve is a straight line.)
(12 pts)
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General Physics I Lab
M10 Standing Waves on a Vibrating String
D. Summary of the experiment (14 pts)
Summarize what you have done and your interpretation of the results, especially in respect to
how they match the goal of the experiment and what you have learned from this experiment
(2-3 paragraphs, less than 450 words).
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