Speed of Sound

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  • Topic: Sound, Loudspeaker, Vernier scale
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  • Published : April 13, 2013
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Title: Measuring the speed of sound.
Research question: How to determine the speed of sound by using the relationship between the frequency of the signal generator, f and the length of air column in the tube, l . Variables:

Manipulated| Frequency of the signal generator, f| Use different frequency of signal generator which are 1000Hz, 1400Hz, 1800Hz, 2000Hz, 2500Hz, 3000Hz and 3600Hz.| Responding| Length of air column in the tube, l (±0.5cm)| Measure the length of the air column in the tube using a metre-rule.| Constant| The volume of water, VAtmospheric pressure, atm (±0.1 Hgcm)Temperature, T (±0.5oc)Diameter of the resonance tube, D (±0.01cm)| Use the same water when conducting the experiment.The experiment is conducted at the same place so that the atmospheric pressure is fixed which is 75.6 Hgcm.The experiment is conducted at the same place so that the temperature is fixed which is 30.05ocThe diameter of the resonance tube is fixed to 2.18cm| Table 1: Manipulated, responding and constant variable.

Apparatus and Materials:
Apparatus and materials| Quantity|
Signal generator| 1|
Loudspeaker| 1|
Resonance tube| 1|
Retort stand with clamp| 1|
Delivery tube| 1|
Barometer| 1|
Vernier caliper (±0.01cm)| 1|
Metre-rule (±0.5cm)| 1|
Highlighter| 1|
Water| -|
Table 2 : The Apparatus and materials.

Method:

The atmospheric pressure is measured using the barometer. The diameter of the resonance tube is measured using the vernier caliper. The resonance tube is connected to a flask using a delivery tube. The resonance tube is clamped to a retort stand. The loudspeaker is connected to the signal generator. The frequency of the signal generator is set to 1000Hz and the loudspeaker is located near the open end of the tube. By using the flask, the length of the air column inside the resonance tube is adjusted until the resonances occur. The resonance is indicated by the increased of sound levels. The length of the air column in the tube, l is measured. The values of l and f is recorded in an appropriate table. A graph is plotted to determine the value of speed of sound, v and the end-correction, e. The values of speed of sound, v and the end-correction, e is obtained by using the formula: λ4= l + e

Data Collection:
Qualitative data:
1) The level of air column in the tube increase when the flask is raised up. 2) The level of air column in the tube decrease when the flask is lowered down. Quantitative data:
Frequency of the signal generator, f (Hz)| Length of air column in the tube, l (±0.05cm)| 1000 (±25)| 6.40|
1400 (±25)| 4.60|
1800 (±50)| 3.20|
2000 (±50)| 2.90|
2500 (±50)| 2.40|
3000 (±100)| 1.40|
3600 (±100)| 1.00|
Table 3:The Frequency of the signal generator, f and Length of air column in the tube, l (±0.5cm) Data Processing:
1Frequency of the signal generator , f-1 (Hz-1)| Length of air column in the tube, l (±0.0005m)| 0.001000 (±0.000025)| 0.0640|
0.000714 (±0.000013)| 0.0460|
0.000556 (±0.000015)| 0.0320|
0.000500 (±0.000013)| 0.0290|
0.000400 (±0.000008)| 0.0240|
0.000333 (±0.000011)| 0.0140|
0.000278 (±0.000008)| 0.0100|
Table 4
Calculation:
*All example shown are from the first data in table 3 and table 4. 1) 1Frequency of the signal generator , f-1
= 11000
= 0.001000 Hz-1
Uncertainty,
Δf-1 = Δff f--1
= 251000 0.001000
= ±0.000025 Hz-1

2) Conversion of length of air column in the tube from cm to m = 6.40 ÷ 100
=0.0640m
Uncertainty,
Δm = Δcmcmm
= 0.056.40 0.064
= ±0.0005m
3) Speed of sound, v

Based on the formula:

λ4= l + e and v = f λ
It can be derived to:
v = f λ λ4 = l + e ______ 2 vf = λ ____ 1
Sub 1 into 2:
vf4 = l + e...
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