Processed Data
l= observed resonating length
L= corrected resonating length
Diameter of tube= 3.54 cm
Radius= 3.54/2 = 1.77cm
End-Correction= 0.6 x r
=0.6 x 0.0177
=0.01062
The slope of the graph is 0.01075
To find the average speed , 1/slope x 4
= (1/0.01075) x 4
= 372 m/s
Calculation of speed of sound for all the lengths:
- L+ e = v/4f
0.33 + 0.01062 = v/4 x 256
V= 348 ±0.005 m/s
- 0.295 + 0.01062= v/4 x 288
V=352 ± 0.005 m/s
- 0.265 + 0.01062= v/4 x 320
V= 352 ± 0.005 m/s
- 0.221 + 0.01062 = v/4 x 384
V= 355 ± 0.005 m/s
- 0.199 + 0.01062 = v/ 4 x 426
V= 357 ± 0.005 m/s
- 0.177 + 0.01062 = v/ 4 x 480
V= 360 ± 0.005 m/s
- 0.165 + 0.01062 = v/4 x 512
V= 359 ± 0.005 m/s
Average speed = Addition of all speeds / Number of speeds
= (348 + 352 +352 + 355 + 357 + 360 + 359) / 7
= 354 m/s
Conclusion
From the graph it is seen that as we take tuning forks of higher frequency the length of the top of the tube from the top layer of the water decreases. It can be clearly stated that the length of the tube is inversely proportional to the frequency of the tuning fork. The data related to the question agrees as the speed of the sound in the resonance can be found with the formula .
L + e = v/4f
Where
L= length of tube from the top layer of water
E= end of correction
V= speed of sound in resonance tube
F= frequency of tuning fork
End correction is the anomal difference between the frequency of a tuning fork and the corresponding sound waves inside of a tube. It is caused because generally there is space between the fork and the pipe end, causing the air column to vibrate a short distance beyond the edge of the tube.
The formula for end correction is
= 0.6 x radius
Where radius = 1.77cm when measured with the use of a vernier caliper.
Evaluation
- There is a ±0.1 error in the graph. After drawing the slope it can be seen that most points pass through or are pretty close to it.
- The data given is very much sufficient to address the practical question.
- Possible errors that may occur would be human errors because the sound heard may not be the loudest but still recorded or maybe writing down the incorrect frequency or length. There might be a systematic error such as a defected tuning fork or resonance tube.
Improving the Investigation
- Trying the experiment more than one time to reduce error.
- Work in a group to make sure everyone can hear the sound.
