Lab 6: Lecture Lab (3/16/2012) s

Purpose:

In this lab we will measure the angular velocity of a spinning pipe in two distinct harmonic to deduce the length of the pipe.


Method:

We will determine the modes of a harmonic through solving the unknown n  by equating the length of the pipe represent by L = n(λ/2) and L = (n+1)*(λ/2). The wavelength will be measure through the angular velocity of the pipe using logger pro. Once n is determined, we can substitute the mode into the length equation to calculate L.


Data and Analysis:

 

Figure 1: Calculation of the length of the pipe. 

ƒ = ω/ 2π

λ = v / ƒ 

μ ƒ  = μω/ 2π

μλ = (v / ƒ_max) - (v / ƒ_min)

Table 1: Measurements from spinning pipe

Harmonic	ω(rad/s)	ƒ(Hz)	λ(m)
Low	3859 ± 0.51	614.49± 0.08	0.5598 ± 0.000145
High	5068 ± 1.10	807.01 ± 0.18	0.425 ± 0.0000845

Figure 2: Calculation of the length of the pipe. 

L = (n₁ / 2) *λ₁

L = ((n₁+1) / 2) *λ₂

n₁ = 3.1 ≈ 3 

(Harmonics are whole numbers)

Substitute n

and

μL =  (μλ / 2) * 3

L = 0.8397 ± 0.0002175 m

Conclusion:

In this lab we have determined the length of the pipe by measuring the angular velocity of two distinct harmonics. The length of the pipe is inversely related to the frequency of the harmonics. Thus by equating the two standing wave equation in terms of length we were able to determine the n of the harmonics and deduce the length of the pipe. We have calculated our uncertainty by setting an upper and lower bound on the calculations. The range between the bound will serve as the uncertainty. We believe that the error in the can be entirely attribute to the precision of the lab equipment.