Speed of Sound Lab

Purpose:

            The purpose of this procedure is to determine if we can accurately measure the speed of sound using with only a microphone and a long cylindrical pipe with one end closed and logger pro.

Procedure:

1.      The following equipment was collected:

a.       Long cylindrical tube

b.      Microphone

c.       Computer

d.      Meter stick

e.       LoggerPro

2.      The microphone was set up to the computer and LoggerPro

3.      The cylindrical tube was then measured using a meter stick

   

4.      Once the meter stick was measured, the microphone set up, and the software prepped to record data, the microphone was placed in front of the open end of the tube while somebody prepared to snap their fingers.

5.      The record button was pressed and the snap was made. This snap must be as brief as possible. This is because if the noise is too long, the recorded initial sound will overlap with the return echo and the differences in peak will not be noticeable. 

6.      The recorded data was then collected and graphed.

7.      Once the graph was collected, we took the time interval from two peaks and recorded them.

Data Analysis:

The time intervals that were recorded are as followed:

t₁ = .00086 s

t₂  = .00738 s

these times were then subtracted from each other to find the total amount of time it took for the sound wave to travel from the microphone initially to when it bounced off of the end of the tube and traveled back (its echo).

Δt = t₂ – t₁ = .00738s - .00086s = .00652s

this calculated time interval is then the time it took for the sound to travel from the edge of the tube to the closed end, and back to the opened end and into the microphone for recording.  All that is needed to find the speed of sound is then to use the simple distance formula with time representing the change found previously and distance double the length of the tube that was recorded earlier (doubled since the wave traveled the length of the tube twice, once to the closed end then back again to the open end).

l = 103.5 ± .25 cm = 1.035 ± .0025 m

t = .00652 s

D = v_s * t

v_s = D/t = 2l / t = (2* 1.035m) / .00652 s

v_s = 317.5 m/s

we will now compare this calculated experimental value of the speed of sound to the theoretical speed of sound. This is done by using the following equation:

v_s  = 331 + .06T

where T is the temperature of the room. For this experiment, the temperature of the room was found to be about 20^oC. Then, the calculation is as followed:

v_s = 331 + .06(20) = 343m/s

obviously, these values do not agree with each other. The percent error between these two can be found for further comparison.

%error = |v_s actual – v­_s exp|/ v_s actual = |343 – 317.5|/343 = 7.43%

Conclusion:

            Although the measured value of the speed of air is not as precise as I would have hoped, the measured experimental value yields a relatively small percent error to the actual value. Reasons for this measurements being off can range from a number of things. The most probably of reasons is most likely that the data sample was not precise enough for these types of calculations. We were dealing with very tiny time frames and the software or microphone may not have been able to pick up the precise time in between echoes. Or perhaps, it could have been human error in which we did not take the peaks sample in the best spot or maybe instead of an echo from the original snap, we could have matched the second time interval to another outside source.