Experiment 3

Exp 3
Wavelength vs frequency



The purpose of this lab was to determine the relationship of waves' period, frequency, and wavelength.

Materials:
Simply,
     A spring
     A timer
     A measuring stick

Procedure:

Some thoughts...

A spring was oscillated consistently for 5 seconds. The length of the measured string was about 1 m long. The period would be found. Meanwhile, the spring's crests was observed to count how many waves throughout the entire oscillation. From those data, velocity could also be found using this relationship:

v = λf

Data, calculations, and errors:

Time, t, was 5.0 +/- 0.1 s throughout.

The quantity of how many times waves were seen to pass through was as seen on the side:

Trial 1: 13 waves +/- 0.25

Trial 2: 11 waves +/- 0.25

Trial 3: 11 waves +/- 0.25

The error was found using partial derivatives.

T (waves, t) = waves / t.

∂T/∂waves = 1/ut

∂T/∂t = - uwaves / ut^2

uT = squareroot of the sum of squares 

Period of each trial:

uT = 3.53. Since the data for all 3 trials are the same, the period's uncertainties, uT, are all the same, 3.53.

Period, T, is #waves / time (5s)

Trial 1 = 2.6 Hz +/- 3.53

Trial 2 = 2.2 Hz +/- 3.53

Trial 3 = 2.2 Hz +/- 3.53

Frequency is the inverse of Period

f = 1/T

f(T) = 1/T

∂f/ ∂T = - 1/T^2

the error for frequency is 

Trial 1 = 0.38 s +/- 0.08

Trial 2 = 0.45 s +/- 0.08

Trial 3 = 0.45 s +/- 0.08

Velocity is the product of wavelength. There were 2.5 waves observed throughout the three trials.

Since the length was 1 m, λ = 1/2.5 = 0.4 m +/- 0.35

(0.35 was obtained by summing all the errors together: 0.25 from waves uncertainty and 0.1 from length uncertainty)

Velocity for each trial is as follows:

v (λ, f) = λ* f

The sum of the errors, 0.35 + 0.08, is 0.43

Trial 1 = 0.15 m/s +/- 0.43

Trial 2 = 0.18 m/s +/- 0.43

Trial 3 = 0.18 m/s +/- 0.43

Error analysis:

The graph has a vertical line. This is because the experiment was done on the same time, 5 second. 

It should have been done through varying time, so the graph would look linear with real slope (slope shown here is infinity). 

All of the values look very similar / the same because again, due to the same time period. 

Another source of error would be when measuring the wavelength through observation. The entire system was in dynamic; the spring was constantly moving. It was hard to measure how many waves were observed at that moment. The 2.5 waves were simply an estimation. It would have been more accurate if a photograph of the spring was taken when oscillated and the number of crests could be counted to obtain a more accurate quantity of wavelength.