Lab 10
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Dec 6, 2023
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Lab 10 Resonance
© 2023 Lone Star College.
All Rights Reserved.
1
Name: _________
Objective
Materials
To observe the properties of resonance tubes.
•
Variable length resonance tube
•
Water
•
1024 Hz tuning fork
•
2048 Hz tuning fork
•
Rubber mallet
Procedure:
In this lab, you will send a sound wave down a tube almost full with water.
You vary the length of
the air column (above the water level) in the tube by changing the
level of water in the tube until you create a standing wave that amplifies the sound. Each
frequency will create an antinode at the tube opening and a node at the water surface for
four lengths. Each length corresponds to a different harmonic.
1.
Before starting the experiment, you should compute the theoretical values of the
tube lengths where you are creating standing waves. Using an estimated speed of
sound of 345 m/s, compute the expected tube lengths using the following
equation for two different frequencies, 1024 Hz and 2048 Hz:
f
n
= n (v/4L)
=
1, 3, 5, …
When n = 1
f
1
= (v/4L);
L = v/(4f
1
)
f=1024 Hz, v=345 m/s;
L = 345/(4 * 1024) = 0.084 m = 8.4 cm
f=2048 Hz, v=345 m/s;
L = 345/(4 * 2048) = 0.042 m = 4.2cm
Lab 10 Resonance
© 2023 Lone Star College.
All Rights Reserved.
2
Compute the theoretical tube lengths required for the first, third, fifth, and
seventh harmonics (n= 1, 3, 5 and 7) at each of the two frequencies. (These
lengths will give you approximate points where you should get resonance)
Record these theoretical values in Table 1.
Data and calculations:
Table 1 - Theoretical Length of Resonance Tubes
1s
t
Harmonic
3rd Harmonic
5
th
Harmonic
7
th
Harmonic
Theor.
Exp
Theor
Exp
Theor
Exp
Theor
Exp
1024 Hz
8.4cm
8.5cm
25.2cm
25.1cm
42.1cm
42.1cm
58.9cm
59.0cm
2048 Hz
4.21 cm
4.2cm
12.6cm
12.7cm
21.0cm
21.2cm
29.48 cm
29.5cm
2.
Fill the resonance tube with water. Practice varying the height of the tube by
moving the water tube up and down. The water level in the tube will rise when
the tub is above the water line, and it will fall when the tube is below the water
line.
3.
Using the rubber mallet, hit the tuning fork. With the tuning fork oscillating, hold
it so that the side of the tuning fork is directly over the top of the tube.
Note:
- Do not hit the tuning fork with anything other than the rubber mallet.
- Hold the tuning fork as close to the opening of the tube as possible, but do not
touch the tube.
4.
Vary the length of the tube until you hear a standing wave amplification of the
tuning fork for the first harmonic. Use your previously calculated theoretical
values of tube length to help you find the approximate location of the water level.
Record the actual/experimental length of the tube in Table 2 below.
Lab 10 Resonance
© 2023 Lone Star College.
All Rights Reserved.
3
5.
Since this is an online lab, watch
“
Resonance - Data Collection Video: and record
the actual lengths of the tube corresponding to 4 harmonics for each tuning fork
and record the data in Table 2 below.
6.
Compare the Theoretical values with experimental value of the length of tubes.
TABLE 2 - Experimental Length of Resonance Tubes:
1s
t
Harmonic
3rd Harmonic
5
th
Harmonic
7
th
Harmonic
Exper.
Theor
Exp
Theor
Exp
Theor
Exp
Theor
Exp
1024 Hz
8.4cm
9.2cm
25.36cm
25.1cm
42.11cm
41.9cm
58.95cm
58.8cm
2048 Hz
4.21cm
4.2cm
12.63cm
12.8cm
21.05cm
21.3cm
29.47cm
29.5cm
1.
For each of the "Experimental" lengths above, calculate the speed of sound
using the equation in procedure step1 above. Record the results in Table 3
below.
Example: f
1
= (v/4L)
v= f
1
* 4 L
1exp
where
“
f
1
= 1024 Hz
”
and
“
L
1exp
“
is the
experimental length from the above table for 1st harmonic.
TABLE 3 - Speed of Sound
1s
t
Harmonic
3rd Harmonic
5
th
Harmonic
7
th
Harmonic
1024 Hz
348.16ms-1
348.11ms-1
352.25ms-1
345.23ms-1
2048 Hz
352.256ms-1
241.23ms-1
360.44ms-1
351.08ms-1
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Lab 10 Resonance
© 2023 Lone Star College.
All Rights Reserved.
4
QUESTIONS:
Answer the following post-lab questions.
1.
How close is the speed of sound to the expected value? What can account for the difference?
2.
What are the possible reasons for theoretical values being different than the experimental
values for the
length of the tubes?
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