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Xavier Bourret-Sicotte Physics18/09/2007

Measuring the speed of sound

In this experiment, we will measure the speed of sound.The apparatus consisted of a plastic tube filled with water linked to a water container. Thiscontainer could be displaced vertically in order to change the water level. We would thenmake a tuning fork vibrate above the pipe and change the water level until the resonance wasat maximum intensity.Hypothesis: The velocity of sound is 330 ms -1

, the relationship between velocity, frequencyand wavelength is represented by the formula v=

ƒλ

,

1) Raw data presented

Table 1

Table 1

shows the frequency of the different tuning forks and the length of air needed for maximum resonance. The error on the length was estimated to 0.1 cm as we repeated eachexperiment several times. Note the error on the forks’ frequencies is a mere estimation as theyare accurately calibrated during manufacture. Frequency /HzLength /m

512.00.157480.00.169456.10.178426.60.192406.40.202384.00.215362.00.226341.30.243320.00.260304.40.270288.00.288271.20.308256.00.323Error +/- 0.1error +/- 0.001

2) Data analysis and interpretation

During the experiment, we have created a fundamental standing wave between the surface of the water and the opening of the pipe. The distance measured represents ¼ of the completestanding wave therefore λ

= measured length * 4-From the general formula v=

ƒλ

, we find that velocity of sound in ms

-1

for the first tuningfork experimented is v = 512

∗

0.157

∗

4 = 321.536-Calculating the error for velocity:

∂

v = (

∂λ

/

λ

+

∂ƒ

/

ƒ

)

∗

vFor the first tuning fork:

∂

v = (0.001 / 0.157+0.1/512)

∗

321.536

∂

v = 2.1108 ms

-1

∂

v

≈

2 ms

-1

∴

v

≈

322 +/- 2 ms

-1

-To find the mean velocity we add all values of v and divide the sum by the number of values.A similar process was completed for the mean ∂

v.Results of all processed data are shown in

table 2

Table 2

Frequency Hz

-1

Length m

-1

Velocity ms

-1

∂

velocity +/- ms

-1

512.00.1573222480.00.1693242456.10.1783252426.60.1923282406.40.2023282384.00.2153302362.00.2263271341.30.2433321320.00.2603331304.40.2703291288.00.2883321271.20.3083341256.00.3233311error +/-

0.1error

+/-

0.001

Mean velocity = (322+324+325+328…) / 13

≈

329Mean

∂

v = (2+2+2+2+2+2+1+1+1…)/13

≈

+/- 2 ms

-1

As

v

=

ƒλ

, and

ƒ

=

v

/

λ

, let

v

be constant of 330 ms

-1

then

ƒ

∝

1/

λ

By plotting the graph of Frequency over 1/

λ

we obtain a straight line. The gradient of thisline represents the constant v

and the y-intercept a systematic error. The situation is illustrated by graph 1 Graph 1

y = 313.24x + 16.736200.0250.0300.0350.0400.0450.0500.0550.00.55 0.75 0.95 1.15 1.35 1.55 1.75 1/wavelength m-1

Note that if we add the y-intercept to the gradient we obtain the value of 329.976 ms -1

for thespeed of sound.Moreover, the second best fit line (in red) illustrates the most extreme interpretation of the

Speed of Sound IB Physics HL Lab report

Physics HL coursework 2008Grade 7

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