The objective of this laboratory was to measure the speed at which sound was traveling through the air, using the resonance of longitudinal waves.

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Experiment 13:  Determining the Speed of Sound

Samir Shuman

April 29, 2011

Physics 111-C21


Objective:

The objective of this laboratory was to measure the speed at which sound was traveling through the

air, using the resonance of longitudinal waves.

Equipment used:  

1- Tall glass of water

1- PVC pipe, 10 in

1- Tape measure, 3 m

1- Mercury thermometer

1- Tuning fork, 384 Hz

1- Marker pencil

1- Block of wood

Data:

Data Table 1

Calculations:

In order to find the value of λ (the wavelength), I used the following equation:

λ= 4(L + 0.3d)

I then plugged the values from Data Table 1 in to find the sound wavelength.

λ= 4 (0.218 m + 0.3 * 0.020 m)

λ= 4(0.218 m + 0.006 m)

λ= 4(0.224 m)

λ= 0.896 m

In order to find the experimental value of v (speed of sound), I used the following equation:

v=fλ

I found λ previously by using the formula λ= 4(L + 0.3d).

The value of f (the frequency of the tuning fork) was found written on the side the tuning fork.

I then used the equation to find the speed of sound.

v=fλ

v= 384  Hz * .896 m

v= 344.064 m/s

In order to find the actual speed of sound, I used the following equation (where Tc= room temperature in °C) :

V speed of sound = 331.4 + 0.6Tc m/s

V speed of sound = 331.4 + 0.6(24) m/s

V speed of sound = 345.8 m/s

I found the % error using the following equation:

% error = experimental value – theoretical value    X  100

                   theoretical value

% error = 344.064 m/s – 345.8 m/s    X 100

                345.8 m/s

% error = +- 0.502 %

Error Analysis

The error analysis for this laboratory was a percent difference calculation between the theoretical value of the speed of sound traveling through air and the experimental value.  This calculation is shown above in the previous section.  The percent error was +- 0.502%.  This percent error is low and attributed to random error.  I think the errors may have partially resulted from an idealized equation. Different temperature recordings should make the calculation of the actual speed of sound vary and not be actual, even if the variance is slight because of the idealized and general other values in the equation (331.4 + .06).  I also worried about getting a proper measurement for the length of the water level to the top of the tube at the point were resonance was at its highest. It was difficult to keep my eye on the exact spot of the first harmonic and then take a measurement. These would both account for the percent error I found.  If I conducted this experiment more times, I believe the percent error would be lower.  Additionally, altitude and humidity must have also played a part in the percent error.  I did not realize this until I thought about it the next day.  The altitude and humidity would both affect the density and elasticity of the air.  I believe this would also make the speed of sound slower at higher altitudes and with less humidity and faster at lower altitudes and with higher humidity.

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Discussion:

I believe that this laboratory experiment was extremely beneficial.  The laboratory manual did an adequate job of explaining the mechanics of a sound wavelength.  In previous physics experiments, I would sometimes find it difficult to understand the concept even though I would accurately use a given equation to solve a problem.  This was not the case in this experiment.  I think that I understood the purpose of this laboratory and the mechanics of how to achieve that goal and find the proper value.  I believe that for a physicist this laboratory would be monumentally beneficial because it ...

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