Tylar MooreScience of Acoustics Sec 01Nasser3/18/2013

Measuring the speed of sound: Resonance tube method

In this experiment, we measured the speed of sound.

The apparatus consisted of a plastic tube filled with water linked to a water container. This

container displaced vertically in order to change the water level. We then took tuning fork to

vibrate above the pipe and change the water level until the resonance was at maximum

intensity.

Hypothesis: The velocity of sound is 342 ms-1, the relationship between speed, frequency and

wavelength is represented by the formula c=, Measuring 18.5 degrees Celsius, we used the

equation Cs=331+0.6(). Having 18.5 as our value for , our theory for the speed of sound

comes to 342.1 m/s.

1) Raw data presented

Table 1

Table 1 shows the measurements of the wavelengths of the first, third and fifth harmonics.

The error on the length was estimated to 0.1 cm as we repeated each experiment several

times.

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 complete

standing wave therefore = measured length * 4

-From the general formula c=, we find that speed of sound in ms-1 for the first tuning fork

experimented is c = 10000.0855254 = 342.1

-Calculating the error for velocity: c = (/ + /)v

For the first tuning fork: c = (0.001 / 0.085525+0.1/1000) 342.1

c = 0.00184 ms-1

c 0 ms-1

c 342 +/- 0 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 c.

Results of all processed data are shown in table 2

Table 2

As c=, and =c/, let c be constant of 342.1 ms-1 then 1/

By plotting the graph of Frequency over 1/ we obtain a straight line. The gradient of this line

represents the constant v and the y-intercept a systematic error. The situation is illustrated by

graph 1

Note that if we add the y-intercept to the gradient we obtain the value of 342.1 ms-1 for the

speed of sound.

3) Evaluation

By repeating the experiment using several harmonics of 1000 Hz we have achieved an

accurate measurement of the speed of sound. We are proud to report that our concluding

results did not stray far from the theoretical value of 342.1 ms-1, it appears that the average of

all measurements is 342 ms-1 . The graph plotting frequency over 1/wavelength is a straight

line passing through all points within the error bars. This proves the inverse proportionality

“1/”. Using the error estimation of the gradient found from the second best fit line, our

final result is c= 342.1+/- 0 ms-1

We may conclude that the experiment is a success as we have obtained the expected

values listed in our hypothesis within an acceptable error range.