# Lab Resonance

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```					        Lab: Resonance
CALIFORNIA CONTENT STANDARDS: PHYSICS
Students know how to solve problems involving wavelength, frequency, and wave
speed.

Objective: To observe the resonance phenomenon in an open-end tube and closed-end tube,
and to use resonance to determine the velocity of sound in air at room temperatures.

Introduction: The velocity with which sound travels in any medium may be determined if the
frequency and the wavelength are known. The relationship between these quantities is:

v = velocity of sound
v = f           where f = frequency
 = wavelength

In this experiment the velocity of sound in air is to be found by using tuning forks of known
frequencies. The wavelength of the sound will be determined by making use of the resonance
established between each tuning fork and the air column inside a tube, open or closed.

Wavelength can be measured with either an open-end tube or closed-end tube by measuring the
length of the air column in either the open or closed tube. One can determine the wavelength
(of a tuning fork when resonance is established and measured.

In an open tube, the wavelength is 2L (2 X the tube length). In a closed tube, the wavelength is
4L (4 X the tube length measured from the open end to the water level in the closed end).

Procedure:
Part 1 – Open End Tube
 Obtain two open-tube apparatuses from the lab table. This should include two large diameter
tubes and two smaller diameter tubes. You will need all of these to measure the resonance
for each of the four tuning forks.
 Obtain four tuning forks with differing frequencies.
 Obtain one rubber “hammer” to be used for striking the tuning fork.
 Select the tuning fork with the highest frequency to begin your experiment. Follow it with
the other tuning forks in their respective orders (decreasing frequencies). Recall that as
frequency increases, wavelength decreases, therefore, your tubing will need to get longer as
you progress.
 For the first measurement, take one large diameter tube and place the small diameter tube
inside.
 Strike the tuning fork with the hammer.
 Place the tuning fork over the “mouth” of one end of the open tube. Be sure to orient the fork
so that its tines are parallel to the tubing. As demonstrated.
 Adjust the small diameter tube until you obtain the greatest resonance between the fork and
the vibrating air in the tubes.
 Record the length of the tube from one end to the other.
 This measurement represents ½ the wavelength for that frequency.
 Multiply this measurement by 2 and add 3.8 cm as a “correction factor”. Convert your
centimeter measurement to meters.
 Repeat this procedure using the other three tuning forks.
 Place all your answers in the table provided.

Part 2 – Closed End Tube
 Follow a similar procedure as you did in Part 1 for this section.
 Place the larger of the two tubes (black tube) into a large beaker and fill the tube with water.
   Place the smaller tube (PVC pipe) into the larger tube. This will cause water to overflow the
black tube. Keep the tubes vertically oriented.
   Strike a 512 Hz tuning fork and place it over the opening of the PVC pipe.
   Raise the pipe until you obtain resonance. As demonstrated.
   When resonance is reached you’ll need to measure the distance (cm) between the top of the
PVC pipe and the water level in the black pipe. This is not easy.
   This measurement represents ¼ wavelength for that frequency.
   Multiply this measurement by 4 and add 3.8 cm as a “correction factor.” Convert your
centimeter measurement to meters.
   Repeat this procedure using the other three tuning forks.
   Place all your answers in the table provided.

Results:
Resonance measurements for different tuning forks: Open End Tubing

Tuning fork (Hz)    Resonance           Wavelength (cm)     Wavelength with     Velocity of
length (L)          [2L]                Correction          sound v = f
Factor added
(convert to m)

Resonance measurements for differing tuning fork: Closed End Tubing

Tuning fork (Hz)    Resonance           Wavelength (cm)     Wavelength with     Velocity of
length (L)          [4L]                Correction          sound v = f
Factor added
(convert to m)

Analysis:
Answer the following questions. Data may be shared between lab partners. Analysis questions
should be discussed and answered as a lab group.

1. What was the average velocity for sound for the open-end tube?
2. What was the average velocity for sound for the closed-end tube?
3. If 340 m/s is the expected speed of sound at room temperature, which method provided the
most reliable results?
4. Why do you think one method proved better than the other?
5. If sound has a known velocity of 340 m/s at room temperature, what was your percent error
for your data? % error = (experimental value – expected value/expected value) x 100
6. What problems did you encounter in making your calculations?
7. What would happen if you did not add in the “correction factor” in your measurements?
8. Why do you think there is a correction factor?

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