Name_____________________________
Per________
Lab: Standing Waves on a String
Part A: Finding Harmonic Frequencies
Purpose: A) To determine the how frequency relates to different standing wave patterns.
Overview: In this lab you will use a string vibration system to generate standing waves on strings. In Part
A: You will generate different standing waves patterns (musicians call them “harmonics” or “overtones”)
and try to find a relationship between the different standing waves (“harmonics”) that can be set up on the
string and their frequencies.
In Part B: You will design and run an experiment to determine what variables affect the 2nd harmonic
frequency of the vibrating string.
A vibrating string can vibrate at certain natural frequencies, or “harmonics”. The lowest natural frequency
is called the “1st harmonic”, or “Fundamental frequency”, or f1, It vibrates with one anti-node.
The “2nd harmonic” f2 is a standing wave with two anti-nodes.
The “3rd harmonic” f3 is a standing wave with 3 anti-nodes, and so-on.
Preparation Phase (setting up and powering on the function generator/string vibrator)
1. Hang a 200 g mass from the end of the string.
2. Make sure the “wave generator” is “unlocked”.
3. Digital Function Generator
a. Turn amplitude to minimum (turn counterclockwise)
b. Turn digital function generator “on” (switch is on the back left side)
c. Use “adjust” knob to reduce frequency to .1 Hz (keep turning counterclockwise, it takes a while!)
Name_____________________________
Per________
PART A: Finding the Harmonic Frequencies
HYPOTHESIS ABOUT HARMONIC FREQUENCIES:
State your hypothesis about how the different harmonic frequencies f1, f2, f3, f4 are related mathematically.
If you have difficulty stating a mathematical relationship, try to state a qualitative relationship between the
harmonic numbers and their frequencies. As the number of standing waves (harmonic number) on the
string increases, how is the frequency related?
  Read the instructions for using the string vibration equipment on the first page  
1.
2.
3.
4.
5.
Turn the AMPLITUDE knob all the way down to MIN to start
Turn the Frequency ADJUST knob all the way down to around 1 Hz to start
Now turn the AMPLITUDE knob to the half-way mark (white mark vertical)
Slowly turn the Frequency ADJUST knob up until you see a wave pattern develop
When you see a standing wave, adjust the frequency back-and-forth until you see the maximum
standing wave.
6. Record your observations and sketch the waveform in the PART A Data Table
7. Repeat steps 2 through 6 as you raise the frequency. Complete the table.
PART A: DATA TABLE
HARMONIC
NUMBER
1
2
3
4
5
#WAVE
F
LENGTHS
on String
FREQ
(Hz)
SKETCH OF STRING
Name_____________________________
Per________
GRAPH of HARMONIC # VS. FREQUENCY
On a separate sheet, draw a proper graph of the harmonic number vs. frequency, including slope.
CONCLUSION
Explain your findings and compare them to your hypothesis. What pattern do you observe between
harmonics and their frequency? Show how it fits the mathematical relationship about harmonic
frequencies (look in your notes and textbook for that relationship!)
LAB REPORT for PART A : should include
1. Purpose
2. Hypothesis
3. Data table (with sketches for Part A)
4. Graph of harmonic number vs frequency
5. Conclusion explaining results
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Name_____________________________
Per________
How do you play different notes on a guitar?
PART B: Design an experiment to determine which variables affect the
harmonic frequencies of a vibrating string
OVERVIEW: Sometimes it is useful to be able to set a string vibration to a specific frequency, for example,
a musician wants a guitar to play exact proper notes. There are several different ways to get a string to
vibrate at a specific frequency, and you will choose 3 to investigate.
Discuss with your group and choose 3 independent variables that you think might change the 2nd
harmonic frequency of a standing wave. Select variables that can be tested with the materials and time
available in the classroom.
FIRST HYPOTHESIS : Write your hypothesis about how Variable A might affect the 2nd harmonic
frequency of a vibrating string. ( for example, “The color of the string affects the frequency of a standing
wave on a string. Darker colors strings have a higher harmonic frequency than lighter colors. This is
because darker colors have more vibrational energy in them.”)
SECOND HYPOTHESIS : Write your hypothesis about how Variable B might affect the 2nd harmonic
frequency a vibrating string.
THIRD HYPOTHESIS : Write your hypothesis about how Variable C might affect the 2nd harmonic
frequency a vibrating string.
Name_____________________________
Per________
DESIGN THE EXPERIMENT:
- How are you going to change and test the independent variables you have chosen?
- What data you want to record in order to test your hypothesis?
- Create a data table before you start your experiment so you know what you need to measure.
- What is independent variable? What is the dependent variable?
- Make at least four different variations to the independent variable and test it.
-
SHOW YOUR HYPOTHESES AND DATA TABLE TO YOUR INSTRUCTOR. After he or
she approves it, you may proceed with running your experiment.
RUN THE EXPERIMENT AND RECORD YOUR DATA IN A TABLE
Make sure you record every trial and the value of your variables and results.
GRAPH YOUR DATA with Independent Variable on the horizontal axis and Dependent Variable on the
vertical axis. Draw a best fit line. You should have separate graphs for each Independent Variable.
WRITE YOUR CONCLUSION about your findings and how they compare to your hypothesis. Show how
your results fit the mathematical expression for the 2nd harmonic frequency.
LAB REPORT FOR PART B
1. Purpose
2. 3 Hypotheses
3. Complete Data Table for each independent variable
4. 3 Graphs of Dependent vs. Independent variables
5. Conclusion explaining results
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