Speed of Sound in Air

ℓ = ¼λ and the second resonance: ℓ = ¾λ, solve for the speed of sound using v = ƒλ.

Data

Length of the First and Second Resonances for Each Individual Tuning Fork

v = ƒλ                First Resonance:  ℓ = ¼λ                  Second Resonance:  ℓ = ¾λ

        λ = 4 ℓ                                              λ = (4/3) ℓ

        λ = 4 (0.341m)                                      λ = (4/3) (1.003m)

        λ = 1.364m                                              λ = 1.337m

Wavelength of the First and Second Resonances for Each Individual Tuning Fork

v = ƒλ                      First Resonance:  v = ƒλ                  Second Resonance:  v = ƒλ

        v = (256Hz) (1.364m)                                    λ = (256Hz) (1.337m)

        v = 349.183 m/s                     v = 342.272 m/s

T = 1 / ƒ                                      Average λ = ( λ of First Resonance + λ of Second Resonance) / 2

T = 1 / 256Hz        Average λ = (1.364m + 1.337m) / 2        

T = 0.003906s        Average λ = 1.351m        

Average Wavelength of the First and Second Resonances for Each Individual Tuning Fork

A graph of average wavelength vs. the period will be provided. Note: Uncertainties are too small to be seen and thus are excluded from the graph but however, must be taken into consideration. The graph will be at the end of the lab.

The slope of the graph demonstrates the average velocity of sound found in the class environment.

Velocity of the First and Second Resonances for Each Individual Tuning Fork

Average Velocity (Sum of all velocities / number of velocities added)

(394.183 m/s) + (342.272 m/s) + (337.920 m/s) + (343.040 m/s) + (330.240 m/s) + (339.456 m/s) + (336.160) + (337.920 m/s) + (335.872 m/s) + (342.528 m/s) / 10

= 343.959 m/s

The experimental velocity speed of sound found in the class environment (in the air) was 343.959 m/s.

Error Propagation

Absolute value of (Actual Value – Experimental Value) / (Actual Value) x 100%

(344 m/s – 343.959 m/s) / (344 m/s) x 100%

= 0.0119% error

Evaluation

The percentage error for this experiment was 0.0119%. Overall, this was a well done experiment. Most of the inaccuracies in this experiment should be accounted from the measuring of the ℓ of the first and second resonances. One should also take into consideration that determining of the first and second resonances were done by ear. A final factor that might have played a role in the inaccuracies would be how we measured the length of resonance (the meter stick was moved to match the bottom of the tube to the top of the water surface but the meter stick was not held steadily). A suggestion for improvement would have been to place the meter stick on the ground beside the cylinder of the water and tube and then measure the height of the water (measuring the length of resonance by subtracting the height of water from the height of the tube to minimize inaccuracy). With these errors and suggestions taken into consideration, a repetition of this lab should ensure more accurate results (even though the error was only 0.0119%).