Question
- Leaving Cert. Physics (Higher) 2014: Section A Q3
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Answer
A student used a cylindrical column of air closed at one end and a tuning fork of frequency 512 Hz in an experiment to measure the speed of sound in air.
The following data was recorded:
Length of column of air for first position of resonance = 16.2 cm
Diameter of air column = 1.15 cm
Draw a labelled diagram of the apparatus used in the experiment.
Describe how the first position of resonance was found.
The tuning fork is struck and held above the resonance tube, as shown, with the top of the tube only slightly above the water. The tube is slowly lifted out of the water, while the fork is still vibrating, until a clear note can be heard. This is the first position of resonance.
Using the recorded data, calculate the speed of sound in air.
f = 512 Hz
l = 16.2 cm = 0.162m
d = 1.15 cm = 0.0115m
Speed of sound, c:
Why was it necessary to measure the diameter of the air column?
The wavelength of the sound wave is 4 times that of the vibrating column of air. The vibrating column of air, though, extends slightly above the tube. It has been found that the full length of the column of air is the length of the tube plus 0.3 times the diameter of the tube. This is why the diameter is measured.
Another student carried out the experiment. She measured the length of the column of air for each of the first two positions of resonance but she did not measure the diameter of the air column.
Explain how this second student would find the speed of sound in air.
She could, of course, ignore the issue altogether. Using
, she would still find a reasonably accurate value for the speed of sound.
As she has values of l for two positions of resonance and because the speed of sound can be taken to be a constant, the value for d could be found using algebra:
First position of resonance:
The second position of resonance will be the third harmonic and therefore:
Equating these gives:
As the student has values for l1, l2, she can calculate the value for d and find the speed of sound, as shown above.
The following data was recorded:
Length of column of air for first position of resonance = 16.2 cm
Diameter of air column = 1.15 cm
Draw a labelled diagram of the apparatus used in the experiment.
Describe how the first position of resonance was found.
The tuning fork is struck and held above the resonance tube, as shown, with the top of the tube only slightly above the water. The tube is slowly lifted out of the water, while the fork is still vibrating, until a clear note can be heard. This is the first position of resonance.
Using the recorded data, calculate the speed of sound in air.
f = 512 Hz
l = 16.2 cm = 0.162m
d = 1.15 cm = 0.0115m
Speed of sound, c:
Why was it necessary to measure the diameter of the air column?
The wavelength of the sound wave is 4 times that of the vibrating column of air. The vibrating column of air, though, extends slightly above the tube. It has been found that the full length of the column of air is the length of the tube plus 0.3 times the diameter of the tube. This is why the diameter is measured.
Another student carried out the experiment. She measured the length of the column of air for each of the first two positions of resonance but she did not measure the diameter of the air column.
Explain how this second student would find the speed of sound in air.
She could, of course, ignore the issue altogether. Using
, she would still find a reasonably accurate value for the speed of sound.As she has values of l for two positions of resonance and because the speed of sound can be taken to be a constant, the value for d could be found using algebra:
First position of resonance:
The second position of resonance will be the third harmonic and therefore:
Equating these gives:
As the student has values for l1, l2, she can calculate the value for d and find the speed of sound, as shown above.