Date __________
Lab Time ______
Name ___________________________
Wave Motion
Objective
This laboratory examines the principle on which most musical instruments operate and
allows the student to observe standing waves, hear resonance and calculate the velocity of the
waves.
Background
Music is based on the relative pitch and quality of sound waves produced by voice or musical
instruments. Nearly all sounds emanating from musical instruments are the result of standing
waves. Two wave trains of the same frequency traveling in the same medium in opposite
directions may produce standing waves. This can be demonstrated by fastening one end to
the string to a post and moving the other end up and down in simple harmonic motion. For a
given frequency the number of loops is determined by the tension in the string. As the wave,
moving to the right, created by the up and down motion of the free end meets the reflected
wave, moving to the left, they interact to form nodes and antinodes. The nodes are points of
no motion, and the antinodes are points of maximum amplitude.
The fundamental principle of wind instruments is the vibration of an air column. Varying the
length of the air column brings about the various notes produced by most wind instruments.
A vibrating tuning fork held in front of the open end of a long pipe with a plunger at the other
end can be made to resonate to the frequency of the fork. This is accomplished by moving
the plunger such that the sound wave traveling down the pipe and the wave reflected off the
plunger constructively interfere and set up standing waves. The length of the pipe for
standing waves depends on the frequency of the vibrating tuning fork.
Materials needed
String vibrator
String
2-Meterstick
weight pan
weights
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Wave Motion
Resonant pipe
Tuning forks (384 Hz & 480 Hz)
Mallet
Meterstick
Clamps and support rods
1
Date __________
Lab Time ______
Name ___________________________
Figure 1
Procedure
Part I. Standing Waves on a String
With the wave generator and string setup, you will adjust the tension in the string (by varying
the weight on the weight pan at the end of the string) to produce standing waves.
1. Measure and record the length, L, of the vibrating string with the 2-meterstick from the
tip of the metal vibrator to where the string touches the top of the pulley.
2. Add or subtract mass on the weight pan until a standing wave is produced and a clear set
of loops are observed.
3. Record the total mass hanging on the end of the string (including the hanger mass).
4. Record the number of loops observed on the string. Figure 1 shows a standing wave with
2 loops.
5. Repeat Steps 2 - 4 to produce 2 more different standing wave patterns (#’s of loops).
Method I: Wave Velocity on a String
2L
, where n
n
is the number of loops observed on the string and L is the length of the string.
6. Calculate and record the wavelength (λ) of the standing waves by using λ =
7. The wave generator vibrates at a constant frequency (f) of 120 Hz. Use this frequency
and the wavelengths for your standing waves to calculate the velocity of the waves on the
string using the wave equation, v = fλ.
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Wave Motion
2
Date __________
Lab Time ______
Name ___________________________
Method II: Wave Velocity on a String
8. Calculate and record the velocity of the wave using the tension on the string (T) and the
T
.
mass per unit length (µ) of the string using the equation v =
µ
-4
(For this string, µ = 3.614 x 10 kg/m and for the Tension, use T = Mg, where M is the
total mass hanging on the end of the string and g is 9.8 m/s2.)
9. Calculate a percent difference in velocity (v) from the 2 different methods.
% difference =
Value 1 − Value 2
* 200%
Value 1 + Value 2
Part II. Resonant Pipe
1. Push the plunger all the way to the end so that it is visible at the end of the pipe. Strike
one of the tuning forks and place it near the opening. Slowly pull the plunger stick
outward until a resonance (loudest sound) is observed.
** You WILL need to frequently strike the tuning fork (to keep it vibrating) while searching for resonance.
2. Once a resonance is located, carefully insert the meter stick into the pipe to measure and
record the length (L1) from the opening of the pipe to the plunger face.
3. Place the same tuning fork at the pipe opening and continue to pull the plunger outward
until a second resonance occurs. Measure and record this new length (L2) from the
opening of the pipe to the plunger face.
4. Repeat Steps 1 – 3 two more times using the same tuning fork.
[Note: All your L1 values should be similar as should all your L2 values.]
5. Calculate the wavelengths (λ) of the sound waves by using λ = 2(L2 – L1).
6. Calculate the velocities of sound (v) in air using the wave equation, v = fλ.
7. Calculate the percent error for each of your velocities of sound using 344 m/s as the
accepted value for the velocity of sound in air.
% error =
Observed Value − Accepted Value
*100%
Accepted Value
8. Calculate the average wavelength (λavg) and average speed of sound (vavg).
9. Repeat Steps 1 – 7 using the second tuning fork.
___________
Wave Motion
3
Date __________
Lab Time ______
Name ___________________________
Report Sheet – Data Analysis
Part I
Length of string (L) __________m
Frequency (f) = 120 Hz
g = 9.8 m/s2
µ = 3.614 x 10-4 kg/m
Method I
# loops (n)
λ (m)
v from f & λ
Mass (kg)
Method II
v from T
% difference
Calculations:
Part II
First tuning fork: f = _______ Hz
L1 (m)
λ (m)
L2 (m)
λavg = ______ m
Calculations:
v (m/s)
% error
vavg = _______ m/s
Second tuning fork: f = _______ Hz
L1 (m)
Calculations:
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Wave Motion
L2 (m)
λ (m)
λavg = ______ m
v (m/s)
% error
vavg = _______ m/s
4
Date __________
Lab Time ______
Name ___________________________
Post-lab questions:
1. How did the mass on the end of the string effect the number of loops you observed?
2. How did the velocity of the wave on the string change with number of loops?
3. How did the wavelengths change for the tuning forks as the frequencies increased?
4. What would you have to do in order to get the next resonant sound out of the pipe?
5. How did your averages for the speed of sound in Part II for each tuning fork compare
with the actual speed of sound (344 m/s) for our room temperature? Comment on the
accuracy and precision of your results.
6. What are some of the possible sources of error in both parts of this experiment?
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Wave Motion
5
Date __________
Lab Time ______
Name ___________________________
Summary/Conclusions:
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Wave Motion
6