Jonathan Alevy

Physics 1302.101

Partners names: Henry Haws, Johnathan Rios & Miguel Castellano

Pre-Lab

Direct Calculation of the Linear Mass Density

1. Measure the mass of a known of the string. Length = L = 1.77 meters

Mass = M = 5.7 x 10-4 kilograms µ = mass/length = 5.7 x 10-4 / 1.77m= 3.22 x 10-4 kg/m

Table 1: Change Tension – Constant Frequency and Length

Frequency = 120 Hz

Length = 1.0 m

Segments, n

Experimental Mass (kg)

Theoretical Mass (kg)

% difference: Exp-Theo

Tension, T (N)

1/n2

1

1.84

1.89

2.78%

18.0

1.00

2

0.463

0.473

2.14%

4.54

0.250

3

0.207

0.210

1.44%

2.03

0.111

4

0.113

0.118

4.33%

1.11

0.0625

5

0.0720

0.0760

5.41%

0.706

0.0400

Slope= 18

The slope is equal to = 18; = 3.125 x 10-4 kg/m

Linear mass density = 3.125 x 10-4 kg/m

Table 2: Vary Frequency

Tension = 4.9 N Tension = Mass x Gravity = 0.500kg x 9.81m/s2 = 4.9 N

Length = 1.0 m

Segments, n

Experimental Frequency (Hz)

Theoretical Frequency (Hz)

% difference Exp-Theo

0

0

0

0%

1

62.00

61.68

0.520%

2

125.7

123.4

1.88%

3

189.0

185.0

2.12%

4

251.1

246.7

1.76%

5

313.9

308.4

1.77%

Slope = 62.9

The slope is equal to = 62.9; =3.096 x 10-4 kg/m

Linear mass density = 3.096 x 10-4 kg/m

Table 3: Results

Method

Linear mass density

% difference

Direct

3.22 x 10-4

Tension vs. 1/n2

3.125 x 10-4

3.0%

Frequency vs. n

3.096 x 10-4

4.0%

Questions

1. As the tension is increased, does the number of segments increase or decrease when the frequency is kept constant?

The number of segments decreases as tension increases